In algebraic geometry, a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold Failed to parse (Missing texvc executable; please see math/README to configure.): M

into projective space. An  ample line bundle is one such that some positive power is very ample. Globally generated sheaves are those with enough sections to define a morphism to projective space.

Introduction[link]

Inverse image of line bundle and hyperplane divisors[link]

Given a morphism Failed to parse (Missing texvc executable; please see math/README to configure.): f\ :\ X \to Y , any vector bundle Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal F

on Y, or more generally any sheaf in Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal O_Y
modules, eg. a coherent sheaf, can be pulled back to X, (see Inverse image functor). This construction preserves the condition of being a line bundle, and more generally the rank. 

The notions described in this article are related to this construction in the case of morphisms to projective spaces

Failed to parse (Missing texvc executable; please see math/README to configure.): f : X \to \mathbb P^N,

and Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal F = \mathcal O(1) \in \mathrm{Pic}(\mathbb P^N)

, the line bundle corresponding to the hyperplane divisor, whose sections are the 1-homogeneous regular functions. See Algebraic geometry of projective spaces#Divisors and twisting sheaves.

Sheaves generated by their global sections[link]

Let X be a scheme or a complex manifold and F a sheaf on X. One says that F is generated by (finitely many) global sections Failed to parse (Missing texvc executable; please see math/README to configure.): a_i \in F(X) , if every stalk of F is generated as a module over the stalk of the structure sheaf by the germs of the a_i. For example, if F happens to be a line bundle, i.e. locally free of rank 1, this amounts to having finitely many global sections, such that for any point x in X, there is at least one section not vanishing at this point. In this case a choice of such global generators a₀, ..., a_n gives a morphism

f: X → Pⁿ, x ↦ [a₀(x): ... : a_n(x)],

such that the pullback f*(O(1)) is F (Note that this evaluation makes sense when F is a subsheaf of the constant sheaf of rational functions on X). The converse statement is also true: given such a morphism f, the pullback of O(1) is generated by its global sections (on X).

Very ample line bundles[link]

Given a scheme X over a base scheme S or a complex manifold, a line bundle (or in other words an invertible sheaf, that is, a locally free sheaf of rank one) L on X is said to be very ample, if there is an immersion i : X → Pⁿ_S, the n-dimensional projective space over S for some n, such that the pullback of the standard twisting sheaf O(1) on Pⁿ_S is isomorphic to L:

i^*(O(1)) ≅ L.

Hence this notion is a special case of the previous one, namely a line bundle is very ample if it is globally generated and the morphism given by some global generators is an immersion.

Given a very ample sheaf L on X and a coherent sheaf F, a theorem of Serre shows that (the coherent sheaf) F ⊗ L^⊗n is generated by finitely many global sections for sufficiently large n. This in turn implies that global sections and higher (Zariski) cohomology groups

Hⁱ(X, F)

are finitely generated. This is a distinctive feature of the projective situation. For example, for the affine n-space Aⁿ_k over a field k, global sections of the structure sheaf O are polynomials in n variables, thus not a finitely generated k-vector space, whereas for Pⁿ_k, global sections are just constant functions, a one-dimensional k-vector space.

Definitions[link]

The notion of ample line bundles L is slightly weaker than very ample line bundles: L is called ample if some tensor power L^⊗n is very ample. This is equivalent to the following definition: L is ample if for any coherent sheaf F on X, there exists an integer n(F), such that F ⊗ L^⊗n is generated by its global sections.

An equivalent, maybe more intuitive, definition of the ampleness of the line bundle Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal L

is its having a positive tensorial power that is very ample. In other words, for Failed to parse (Missing texvc executable; please see math/README to configure.): n \gg 0 
there exists a projective embedding Failed to parse (Missing texvc executable; please see math/README to configure.): j: X \to \mathbb P^N
such that Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal L^{\otimes n} = j^* (\mathcal O(1))

, that is the zero divisors of global sections of Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal L^{\otimes n}

are hyperplane sections.

This definition makes sense for the underlying divisors (Cartier divisors) Failed to parse (Missing texvc executable; please see math/README to configure.): D

an ample Failed to parse (Missing texvc executable; please see math/README to configure.): D

is one where Failed to parse (Missing texvc executable; please see math/README to configure.): nD
moves in a large enough linear system. Such divisors form a cone in all divisors of those that are, in some sense, positive enough. The relationship with projective space is that the Failed to parse (Missing texvc executable; please see math/README to configure.): D
for a very ample Failed to parse (Missing texvc executable; please see math/README to configure.): L
corresponds to the hyperplane sections (intersection with some hyperplane) of the embedded Failed to parse (Missing texvc executable; please see math/README to configure.): M

.

The equivalence between the two definitions is credited to Jean-Pierre Serre in Faisceaux algébriques cohérents.

Criteria for ampleness of line bundles[link]

Intersection theory[link]

To decide in practice when a Cartier divisor D corresponds to an ample line bundle, there are some geometric criteria.

For curves, a divisor D is very ample if and only if l(D) = 2 + l(D − A − B) whenever A and B are points. By the Riemann–Roch theorem every divisor of degree at least 2g + 1 satisfies this condition so is very ample. This implies that a divisor is ample if and only if it has positive degree. The canonical divisor of degree 2g − 2 is very ample if and only if the curve is not a hyperelliptic curve.

The Nakai–Moishezon criterion (Nakai 1963, Moishezon 1964) states that a Cartier divisor D on a proper scheme X over an algebraically closed field is ample if and only if D^dim(Y).Y > 0 for every closed integral subscheme Y of X. In the special case of curves this says that a divisor is ample if and only if it has positive degree, and for a smooth projective algebraic surface S, the Nakai–Moishezon criterion states that D is ample if and only if its self-intersection number D.D is strictly positive, and for any irreducible curve C on S we have D.C > 0.

The Kleiman condition states that for any projective scheme X, a divisor D on X is ample if and only if D.C > 0 for any nonzero element C in the closure of NE(X), the cone of curves of X. In other words a divisor is ample if and only if it is in the interior of the real cone generated by nef divisors.

Nagata (1959) constructed divisors on surfaces that have positive intersection with every curve, but are not ample. This shows that the condition D.D > 0 cannot be omitted in the Nakai–Moishezon criterion, and it is necessary to use the closure of NE(X) rather than NE(X) in the Kleiman condition.

Seshadri (1972, Remark 7.1, p. 549) showed that a line bundle L on a complete algebraic scheme is ample if and only if there is some positive ε such that deg(L|_C) ≥ εm(C) for all integral curves C in X, where m(C) is the maximum of the multiplicities at the points of C.

Sheaves cohomology[link]

The theorem of Cartan-Serre-Grothendieck states that for a line bundle Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal L

on a variety Failed to parse (Missing texvc executable; please see math/README to configure.): X

, the following conditions are equivalent:

• Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal L

is ample

• for m big enough, Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal L^{\otimes m}

is very ample

• for any coherent sheaf Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal F

on X, the sheaf Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal F \otimes \mathcal L^{\otimes m}
is generated by global sections, for m big enough

• for any coherent sheaf Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal F

on X, the higher cohomology groups Failed to parse (Missing texvc executable; please see math/README to configure.): H^i(X, \mathcal F \otimes \mathcal L^{\otimes m}), \ i \geq 1
vanish for m big enough.

Generalizations[link]

Vector bundles of higher rank[link]

A locally free sheaf (vector bundle) Failed to parse (Missing texvc executable; please see math/README to configure.): F

on a variety is called ample if the invertible sheaf Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal{O}(1)
on Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{P}(F)
is ample Hartshorne (1966). 

Ample vector bundles inherit many of the properties of ample line bundles.

Big line bundles[link]

An important generalization, notably in birational geometry, is that of a big line bundle. A line bundle Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal L

on X is said to be big if the equivalent following conditions are satisfied:

• Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal L

is the tensor product of an ample line bundle and an effective line bundle

• the Hilbert polynomial of the finitely generated graded ring Failed to parse (Missing texvc executable; please see math/README to configure.): \bigoplus_{k=0}^\infty \Gamma (X, \mathcal L ^{\otimes k})

has degree the dimension of X

• the rational mapping of the total system of divisors Failed to parse (Missing texvc executable; please see math/README to configure.): X \to \mathbb P \Gamma (X, \mathcal L^{\otimes k})

is birational on its image for Failed to parse (Missing texvc executable; please see math/README to configure.): k \gg 0

. The interest of this notion is its stability with respect to rational transformations.

See also[link]

General algebraic geometry[link]

• Cartier divisor
• Algebraic geometry of projective spaces
• Fano variety: a variety whose Canonical line bundle is anti-ample

Ampleness in complex geometry[link]

• Holomorphic vector bundle
• The Chern class is a characteristic form that detects ampleness of line bundles, this is the
• Kodaira embedding theorem: for compact complex manifolds, ampleness and positivity coincide.
• Lefschetz hyperplane theorem: the study of very ample line bundles on complex projective manifolds gives strong topological information

References[link]

Study references[link]

• Hartshorne, Robin (1977), Algebraic Geometry, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157 
• Lazarsfeld, Robert (2004), Positivity in Algebraic Geometry, Berlin: Springer-Verlag 
• The slides on ampleness in Vladimir Lazić's Lectures on algebraic geometry

Research texts[link]

• Hartshorne, Robin (1966), "Ample vector bundles", Publications Mathématiques de l'IHÉS (29): 63–94, ISSN 1618-1913, MR 0193092, http://www.numdam.org/item?id=PMIHES_1966__29__63_0 
• Kleiman, Steven L. (1966), "Toward a numerical theory of ampleness", Annals of Mathematics. Second Series (Annals of Mathematics) 84 (3): 293–344, DOI:10.2307/1970447, ISSN 0003-486X, JSTOR 1970447, MR 0206009 
• Moishezon, B. G. (1964), "A projectivity criterion of complete algebraic abstract varieties", Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 28: 179–224, ISSN 0373-2436, MR 0160782 
• Nagata, Masayoshi (1959), "On the 14th problem of Hilbert", American Journal of Mathematics (The Johns Hopkins University Press) 81 (3): 766–772, DOI:10.2307/2372927, JSTOR 2372927, MR 0154867 
• Nakai, Yoshikazu (1963), "A criterion of an ample sheaf on a projective scheme", American Journal of Mathematics (The Johns Hopkins University Press) 85 (1): 14–26, DOI:10.2307/2373180, ISSN 0002-9327, JSTOR 2373180, MR 0151461 
• Seshadri, C. S. (1972), "Quotient spaces modulo reductive algebraic groups", Annals of Mathematics. Second Series (Annals of Mathematics) 95 (3): 511–556, DOI:10.2307/1970870, ISSN 0003-486X, JSTOR 1970870, MR 0309940 

Katy Perry
Katy Perry at the Logie Awards in 2011
Background information
Birth name	Katheryn Elizabeth Hudson
Also known as	Katy Hudson
Born	(1984-10-25) October 25, 1984 (age 27) Santa Barbara, California, U.S.
Genres	Pop, rock, dance, gospel
Occupations	Singer-songwriter, actress
Instruments	Vocals, guitar, piano
Years active	2001–present
Labels	Red Hill, Island, Columbia, Capitol
Associated acts	The Matrix
Website	Katyperry.com

Katheryn Elizabeth Hudson^[1] (born October 25, 1984), known by her stage name Katy Perry, is an American singer, songwriter and actress. Perry grew up with gospel music, and during her first year of high school she pursued a music career as Katy Hudson, releasing her first studio album called Katy Hudson which failed to chart. She recorded a solo album later, which was never released. After signing with Capitol Music Group in 2007, her fourth record label in seven years, she adopted the stage name Katy Perry.

She first gained recognition with the release of her first mainstream album, One of the Boys in 2008, which spawned three Billboard Hot 100 top-ten songs—"I Kissed A Girl", "Hot n Cold" and "Waking Up In Vegas". Perry supported the album with her Hello Katy Tour. In 2010, her third studio album, Teenage Dream (2010), which topped the Billboard 200 chart, and spawned five number one singles—"California Gurls", "Teenage Dream", "Firework", "E.T." and "Last Friday Night (T.G.I.F.)"—Teenage Dream was the only album (after Michael Jackson's Bad)—to do so, and the first female in history to achieve this milestone. She embarked on the California Dreams Tour, which grossed nearly $60 million worldwide.^[2] Perry re-released the album under the name of Teenage Dream: The Complete Confection on March 26, 2012, and the re-release has already spawned the number-one single "Part of Me".

Perry is the only artist to spend over 52 consecutive weeks in the top ten of the Billboard Hot 100, and has since heightened this to 69 weeks.^[3] As of 2012, Perry has been nominated for eight Grammy Awards. She was named 2011's "Artist of the Year" by MTV.^[4] She has sold 37.6 million digital tracks in the United States and 11 million albums worldwide.^[5] Perry was a guest judge on the seventh series of The X Factor UK and the ninth season of American Idol. She has released fragrances "Purr" and "Meow". She ventured into film, voicing Smurfette in the 2011 film The Smurfs. Perry was married to British comedian Russell Brand from 2010 to 2012.

Early life[link]

Perry was born Katheryn Elizabeth Hudson in Santa Barbara, California^[6] to Keith, a West Coast scenester in the 1960s,^[7] and Mary Hudson (née Perry), an evangelist who grew up in Southern California and had a "tempestuous" first marriage in Zimbabwe.^[7] Perry has Portuguese, German, Irish, and English ancestry.^[8][9][10] She is the second child of two pastors.^[11] She has an older sister named Angela Hudson and younger brother named David Hudson.^[12] Perry's mother's aunt and uncle were screenwriter Eleanor Perry and director Frank Perry.^[7] Perry was incorporated into her parents' ministry^[11] and sang in their church between the ages of 9 and 17.^[13] She grew up listening to gospel music,^[14] was not allowed to listen to what her mother called "secular music",^[13][15] and attended Christian schools and camps.^[11] As a child, Perry learned how to dance in a recreation building in Santa Barbara. She was taught by seasoned dancers and began with swing, Lindy Hop, and jitterbug.^[16] She took her GED after her first year at Dos Pueblos High School and decided to leave school in the pursuit of a career in music.^[17] Perry initially started singing "because [she] was at that point in [her] childhood where [she] was copycatting [her] sister and everything she [would do]."^[17] Her sister practiced with cassette tapes, while Perry took the tapes herself when her sister was not around. She rehearsed the songs and performed them in front of her parents, who suggested she take vocal coaching. She grabbed the opportunity and began taking lessons at the age of nine and continued until she was sixteen. She later enrolled in at the Music Academy of the West in Santa Barbara, and studied Italian opera for a short period of time.^[17]

Career[link]

1999–2006: Career beginnings[link]

Perry performing on her guitar, an instrument she learned to play when she was just starting her record career

When Perry was 15, her singing in church attracted the attention of rock veterans from Nashville, Tennessee, who brought her there to polish her writing skills.^[18] In Nashville, Perry started recording demos and was taught by country music veterans how to craft songs and play guitar.^[13][15] Perry signed to the Christian music label Red Hill, under which she recorded her first album at the age of 15.^[19] Performing as Katy Hudson, she released a self-titled gospel rock album in 2001.^[18] She supported this album with The Strangely Normal Tour, accompanied by Phil Joel, LaRue, Luna Halo, Earthsuit and V*Enna.^[20] The album was unsuccessful as the label ceased operations at the end of 2001.^[19] She later changed her surname to Perry, her mother's maiden name, because "Katy Hudson" was too close to film actress Kate Hudson.^[18][21]

Perry performs at the 2008 Warped Tour

At the age of 17, Perry left her home for Los Angeles, where she worked with Glen Ballard on an album for Island Records.^[22] Growing up listening to mostly gospel music, Perry had few references when she began recording songs.^[13] Asked by the producer with whom she would like to collaborate, Perry had no idea. That night, she went with her mother to a hotel. Inside, she turned on VH1 and saw producer Glen Ballard talking about Alanis Morissette;^[13] Ballard produced Morissette's Jagged Little Pill, which had a "huge influence" on Perry.^[18] She expressed interest in working with Ballard to her initial collaborator, who arranged a meeting for her with Ballard in Los Angeles. Perry presented one of her songs to Ballard. Ballard then helped Perry develop her songwriting over the next few years.^[13] The album was due for release in 2005,^[18][19] but Billboard reported it also went nowhere.^[19] Perry was dropped by The Island Def Jam Music Group.^[7] Some of Perry and Ballard's collaborations included "Box", "Diamonds" and "Long Shot", were posted on her official MySpace page. "Simple", one of the songs she recorded with Ballard, was released on the soundtrack to the 2005 film The Sisterhood of the Traveling Pants.^[23][24] "Long Shot" and "I Do Not Hook Up" was later recorded by Kelly Clarkson for her 2009 album All I Ever Wanted.^[25]

Perry signed to Columbia Records in 2004. However, the label was not amenable with her vision, not putting her in the "driver's seat".^[19] Instead, one of Columbia's ideas was to pair Perry with the record production team The Matrix, who was working on an album, to serve as its female vocalist. Although the album was later shelved,^[26] she caught the attention of the music press: Her burgeoning music career led to her being named "The Next Big Thing" in October 2004 by Blender magazine.^[19] With no album project ongoing, Perry began recording her own. Eighty percent completed, however, Columbia decided not to finish it and dropped her from the label.^[19] While waiting to find another label, she worked in an independent A&R company called Taxi Music. In 2006, Perry was featured in the tail-end of the video to P.O.D.'s single "Goodbye for Now".^[27] She made a cameo appearance in Carbon Leaf's video, "Learn to Fly".

[edit] 2007–09: Commercial success with One of the Boys and MTV Unplugged

While in the process of being dropped by Columbia in 2006, the company's publicity executive Angelica Cob-Baehler enthusiastically recommended Perry to Virgin Records chairman Jason Flom.^[28] At the time Flom was leading a complete revival in fortunes at the label and looking to crown recent achievements by breaking a global pop act.^[28] Despite mixed reactions from fellow Virgin executives, Flom became convinced that Perry could be that breakthrough star, and at the start of 2007 extended discussions with Columbia resulted in Perry signing to the newly created Capitol Music Group, a merger between Virgin and Capitol. As part of the deal, the label secured the masters to the unfinished album, recorded while at Columbia, that would go on to form a significant part of her official mainstream debut album, One of the Boys.^[28]

The Columbia recordings were seen by Flom as being "very strong but lacking an undeniable smash or two that would work both at U.S. pop radio and internationally" and so one of the executive's first actions after completing the signing was to set up a collaboration between Perry and the writer-producer Dr. Luke.^[28] The results were the songs "I Kissed a Girl" and "Hot n Cold". Establishing her image was one of the immediate concerns of her management.^[19] A campaign was started in November 2007 with the release of the video to "Ur So Gay", aimed at introducing her to the music market. A digital EP led by "Ur So Gay" was later released to create online buzz and press story.^[11][19][29] This was a successful move that resulted in bringing Perry to the attention of Madonna,^[19] who mentioned her on KISS FM and KRQ's JohnJay & Rich morning show in Arizona. On March 10, 2008, she appeared as herself on the ABC Family television series, Wildfire, on the episode "Life's Too Short".^[30]

Perry during Hello Katy Tour on March 27, 2009

In the next step of promoting the album, Perry undertook a two-month tour of radio stations. The album's official lead single, "I Kissed a Girl", was released on May 6, 2008. Perry's A&R, Chris Anokute, told HitQuarters the song and its controversial theme had met with strong resistance at the label: "People said, 'This is never going to get played on the radio. How do we sell this? How’s this going to be played in the bible belt?'"^[29] Anokute said that they needed the support of one of the label's radio promoters to convince people to believe in the record; otherwise, Perry would have likely been dropped again. Capitol's SVP of Promotions, Dennis Reese, saw the vision and helped push the single on national radio. The first station to pick it up and take a chance was The River in Nashville. After playing it for three days they were innundated with enthusiastic calls.^[29] With the song climbing atop the charts, Perry embarked on the annual Warped Tour music festival, which her management used to "establish her as a credible performer and make sure she wasn't seen as just a one-hit wonder."^[19] The single was a commercial success, peaking at number one for seven weeks on the Billboard Hot 100.^[19] It has since become a major worldwide hit, topping charts in 30 countries,^[26] including Australia, Canada, and the United Kingdom.^[31] On June 12, 2008, Perry appeared as herself on the daytime soap opera The Young and the Restless,^[30] posing for the cover to the June 2008 issue of the fictional magazine Restless Style.^[32] Perry also performed backing vocals on the song, "Another Night in the Hills" from Gavin Rossdale's 2008 solo album Wanderlust.^[33]

One of the Boys was released on June 17, 2008, to mixed critical reviews.^[34] The album has reached number nine on the Billboard 200,^[35] and has been certified platinum by the Recording Industry Association of America.^[36] Perry released her second single, "Hot n Cold", which became her second top three single in dozens of countries around the world, including the United States where it reached number three on the Billboard Hot 100,^[19] as well as topping the charts in Germany, Canada, and Denmark. After Perry wrapped up her appearance at the Warped Tour, she went on tours in Europe. She later launched her first headlining tour, the Hello Katy Tour, in January 2009.^[19] "I Kissed a Girl" earned Perry a nomination for Best Female Pop Vocal Performance at the 2009 Grammy Awards.^[37] Perry was nominated in five categories at the 2008 MTV Video Music Awards, including Best New Artist and Best Female Video, but lost to Britney Spears.^[38] She won Best New Act at the 2008 MTV Europe Music Awards, which she co-hosted,^[39] and Best International Female Artist at the 2009 BRIT Awards.^[40] On February 9, 2009, both "I Kissed a Girl" and "Hot n Cold" were certified three-time platinum by Recording Industry Association of America for individual digital sales of over three million.^[41] The Guinness Book of World Records recognized Perry in its 2010 version as the "Best Start on the US Digital Chart by a Female Artist," for having her first two singles sell over two million digital copies.^[42]

Perry during the Hello Katy Tour in June 2009

The Matrix's self-titled debut album, which features Perry, was later released via the team's label, Let's Hear It, during Perry's solo tour. When the release date was scheduled, "I Kissed a Girl" had been charting well. Matrix member Lauren Christy spoke to Perry about the decision, but she wanted to hold the release until the fourth single of One of the Boys had been dispatched. Despite their communication, The Matrix was released on January 27, 2009, via iTunes Store.^[43]

In December 2008, Perry apologized to British singer Lily Allen for remarks in which she called herself a "skinnier version" of her, saying she meant it as a joke.^[44] Allen retaliated and told a British radio station that she "happen[ed] to know for a fact that she [Perry] was an American version" of her because their record company needed "to find something controversial and 'kooky'" like her.^[45] In January 2009, Perry embarked on her first headlining world tour, the Hello Katy Tour, visiting North America, Europe, Asia, and Australia. Beginning on January 23, 2009, and ending on November 28, 2009, the tour consisted of 89 concerts. During that time, Perry also opened select concerts for the band No Doubt, on their Summer Tour 2009.

On May 16, 2009, Perry performed at the opening ceremony of the annual Life Ball in Vienna, Austria.^[46] In June 2009, lawyers acting for Perry opposed the then-recent trademark of Australian fashion designer Katie Perry, who uses her own name to market loungewear.^[47] Some media outlets reported this as a lawsuit, which Perry denied on her blog.^[48] Katie Perry reported on her blog that at a hearing with IP Australia on July 10, 2009, the singer's lawyers withdrew their opposition to the trademark.^[49] During the summer of 2009 Perry filmed a cameo appearance for Get Him to the Greek; her scene, in which she kisses her future fiancé Russell Brand was cut, and does not appear in the final film. Discussing the issue with MTV, Perry hypothesized there may have been some fear that seeing the two make out would have taken viewers out of the experience.^[50] In 2009, Perry was featured on two singles: in August, a remix of Colorado-based band 3OH!3's song "Starstrukk" (the idea for the collaboration having come after Perry's tour that featured 3OH!3 as the supporting act, the song being released by iTunes on September 8, 2009); and, thereafter, in December, on "If We Ever Meet Again", the fourth single from Timbaland's album Shock Value II.^[51] In October 2009, MTV Unplugged revealed that Perry was one of the artists to perform for them, and that she would be releasing a live album of the performance, including two new tracks, "Brick by Brick" and Fountains of Wayne cover "Hackensack".^[52] The album, released on November 17, included both a CD and a DVD,^[53] and debuted at No. 168 on the US Billboard 200 chart.

[edit] 2010–present: Teenage Dream, film debut and The Complete Confection

Perry at 2011 MTV Video Music Awards

Perry appeared as a guest judge alongside Simon Cowell, Cheryl Cole and Louis Walsh during the Dublin audition stage of the seventh series of the British television show The X Factor on June 28, 2010.^[54] She was one of the many celebrities chosen to fulfil the role of judge whilst Dannii Minogue was on maternity leave. In May 2010, Perry released the first single from her second studio album, Teenage Dream entitled, "California Gurls". The single peaked at number one on the Billboard Hot 100 for six consecutive weeks.^[55][56] "Teenage Dream" was released as the second single from her album, and it also topped the Billboard Hot 100, becoming her third number one and second from the album. Teenage Dream was released August 24, 2010 and debuted atop the Billboard 200 chart with sales of 192,000 copies in its first week.^[57] The album as since sold over 2 million copies in the US, being certified Platinum by the RIAA. Following the album's release, the third single "Firework" was released and became the third consecutive single from Teenage Dream to top the Hot 100. With this, Perry became the first female in eleven years to have three consecutive number-ones from one album.^[58] In February 2011, Perry released the fourth single, "E.T.", a remixed version featuring Kanye West, that peaked at number one on the Billboard Hot 100 for five non-consecutive weeks.^[59] The music video for "E.T." was directed by Floria Sigismondi and features Shaun Ross as the main love interest. With "E.T." at number one on the chart of May 12, 2011, Perry became the first artist to spend 52 consecutive weeks in the top 10 of the Billboard Hot 100.^[3] In June 2011, Perry released the fifth single, "Last Friday Night (T.G.I.F.)". A remixed version featuring American rapper Missy Elliot was released in early August.^[60] The song topped the Billboard Hot 100 on August 17, 2011, making Perry the first female and second artist (tied with Michael Jackson) ever to have five No. 1 singles from one album. Also, when the song reached number 1 in the Pop Songs airplay chart, "Teenage Dream" became the first album to have 5 number 1's from the same album on that chart. Additionally, when the song reached number one in the Adult Pop Songs airplay chart, the album become the first to have 4 number 1's from the same album on the chart.^[61] In October 2011, Perry released the sixth single, "The One That Got Away". It reached No. 3 on Hot 100, becoming the third album in history to produce six top five hit singles,^[62] and the seventh song from Teenage Dream to reach the top of the Billboard Hot Dance Club Songs, the most by any album and setting a new record in the chart.^[63] Perry released a "The One That Got Away" remix featuring American rapper B.o.B. in December 2011. An acoustic version of the song was released in January 2012.^[64]

From February 2011 to January 2012, Perry embarked on an extensive world tour in support of Teenage Dream, the California Dreams Tour, playing 124 shows in Europe, Australasia, Asia, North America and South America and earning over $59 million.^[2] Perry made her perfume debut, releasing a fragrance named "Purr" in November. It is packaged in a cat-shaped bottle, and is available through Nordstrom stores.^[65][66] She followed it up with the fragrance's first flanker, "Meow".^[67][68]

Perry promoting her 2011 fragrance 'Purr'

In July 2011, Perry made her film debut in the 3D family film The Smurfs as Smurfette. The Smurfs earned $557,771,535 worldwide during its theatrical run. Perry appeared at the 2011 MTV Video Music Awards on August 28, 2011. She was nominated for ten awards, received the most nominations of the ceremony and was the first singer to have four different music videos shown in various categories, eventually winning three of those, Video of the Year for "Firework", Best Collaboration and Best Special Effects for "E.T.". On September 17, 2011, marked Perry' 69th consecutive week in the Top 10 with single "Last Friday Night (T.G.I.F.)".^[69][70] On September 23, 2011, she performed, along with Elton John, Brazilian Claudia Leitte and friend Rihanna, on the opening day of the 2011 Rock in Rio festival, which was extended to October 2.^[71] Perry performed for 100 thousand people, a show that received high praise from critics and audience alike.^[72]

On December 14, 2011, the annual list Forbes was elected the third singer who earned more than US$44 million, behind Lady Gaga (US$90 million) and Taylor Swift (US$45 million).^[73] On December 15, 2011, Perry was elected the Artist of the Year by MTV, for their performance on the charts worldwide and won the record during the year.^[4] On December 20, 2011, She released a Barbie doll that represents her style in 2012.^[74] On January 8, 2012, Perry was named the sixth best-selling digital artist of all time in the United States, having sold 37,620,00 million singles and albums as of 2011, according to Nielsen SoundScan.^[75]

In the week ending January 15, 2012, Perry became the first artist ever to have five songs sell over 5 million digital copies in the USA.^[76] Perry was once again recruited by EA Games to promote their new expansion pack The Sims 3: Showtime for their The Sims game franchise. The game content was based on Perry.^[77] Perry became the first person to have six songs top the Billboard Adult Pop Songs chart.^[78] In March 27, 2012, she re-released Teenage Dream under the title Teenage Dream: The Complete Confection on March 27, 2012. The lead single from the re-release (and seventh single from the Teenage Dream era overall) was "Part of Me", which released in February, debuted atop the Billboard Hot 100 chart.^[79] Perry has announced that she will release a part-biopic, part-concert film to be shown in 3D titled Katy Perry: Part of Me to be released on the 4th of July weekend of 2012 by Paramount Pictures.^[80][81] In April 2012, Perry performed in India for the first time at the opening ceremony of 5th edition of Indian Premier League, cricket match, in Chennai along with Indian actors Amitabh Bachchan, Salman Khan, Kareena Kapoor, Priyanka Chopra and Prabhu Deva.^[82][83][84] She performed her songs "Teenage Dream" and a remix version of "California Gurls".^{[85][83][86][87]} In April 2012, Perry stated that she was working on new music and changing her musical style, "My music is about to get real f—ing dark. You'd never see my face because my hair would be in it."^[88]

Artistry[link]

Musical style and themes[link]

Perry performing in 2009

Perry has a contralto vocal range.^[89] Perry's first album is of the Gospel music genre.^[11][19] She related that her perspective in music was "a bit enclosed and very strict", and everything she did was church-related.^[11] Her second album, One of the Boys, is described as "secular" and "rock," and reflects a departure from her religious musical roots.^[11] Her next album Teenage Dream featured more pop songs in the vein of Boys.^[16][90] In her childhood, Perry was introduced to the music of Alanis Morissette and Freddie Mercury, the late frontman of the British band Queen.^[26] In her tribute to Mercury on what would have been his 65th birthday, Perry stated; "Without you I wouldn't be making music or doing what I do because your lyrics inspired me as a 15 year old girl."^[91] Queen's song "Killer Queen" has inspired her to pursue a career in pop music after her first album.^[11] She also described that Morissette's album Jagged Little Pill as having influenced her music profoundly; even going on to work with Morissette's collaborator on the album, Glen Ballard because of that.^[18] Influence also came from a number of female pop rock singers, including Cyndi Lauper, Shirley Manson, Pat Benatar and Joan Jett, as "they came out with a vengeance."^[92] Perry also cited Madonna as another big influence, saying "I want to evolve like Madonna."^[93][94]

	"Part of Me" noicon A 22 second sample of Part of Me, a song with a pop rock influence, which is a common genre for Perry's songs.
Problems listening to this file? See media help.

Perry is artistically involved in her projects, especially in the writing process. Since she could play guitar, she would start writing songs at home and present it to her producers. Perry is mostly inspired by specific moments of her life. She said it is easy for her to write songs about heartbreak.^[13] Most of the themes in One of the Boys deal with heartbreak, teen adventure, and "puking into toilets".^[18] Perry's mother reportedly told British tabloid Daily Mail that she dislikes her daughter's music, calling it "shameful and disgusting".^[11][95] Perry said her mother was misquoted and told MTV that it was false information.^[95] Her songs "Ur So Gay" and "I Kissed a Girl" have received negative reactions from both religious and gay sectors.^[95] The songs have been respectively labeled as being homophobic and promoting homosexuality, as well as "lez ploitational".^[11] Musicians Pink, Kathleen Hanna and Beth Ditto criticized "I Kissed A Girl" as offensive to the LGBT community.^[96][97][98] MTV mentioned criticism suggesting that Perry is using "bi-curiosity" as a way to sell records.^[95] Perry responded to the controversy surrounding "Ur So Gay": "It's not a negative connotation. It's not, 'you're so gay,' like, 'you're so lame,' but the fact of the matter is that this boy should've been gay. I totally understand how it could be misconstrued or whatever ... It wasn't stereotyping anyone in particular, I was talking about ex-boyfriends."^[99] Perry has written several songs for other singers, including Ashley Tisdale ("Time's Up"), Selena Gomez & the Scene ("Rock God" and "That's More Like It"), Kelly Clarkson ("Long Shot" and "I Do Not Hook Up"), Jessica James ("Bullet" and "Girl Next Door"), Lesley Roy ("Slow Goodbye"), and Kady Malloy ("Wish You the Worst").

Public image[link]

Perry is known for her unconventional style of dress.^[16] It is often humorous, bright in color, and reminiscent of different decades, and she frequently uses fruit-shaped accessories, mainly watermelon, as part of her outfits.^[92] Perry's transformation into an artist began with fashion, inspired by American film actress Dominique Swain's portrayal in the 1997 film Lolita.^[18] She defines her fashion style as "a bit of a concoction of different things".^[16] Her fashion has caught the attention of designers.^[11][92] In June 2008, a publicity photo that showed Perry posing with a switchblade was criticized.^[100] The picture was defended as only an effort to give Perry a "sexy, harder edge".^[100] The criticism leveled at her was mocked by Perry who subsequently posed with a spoon instead.^[101] She was ranked 7th in Rolling Stone's global Queen of Pop poll in July 2011.^[102] Perry is also a gay activist. According to Dosomething.org, Perry had stated "I am a gay activist and I say that proudly. I voted no on Prop 8 (California’s Nov. 4, 2008, amendment declaring that marriage is defined as a union solely between a man and a woman), of course."^[103]

Personal life[link]

Russell Brand, Perry's estranged husband

Perry has had relationships with Gym Class Heroes frontman Travie McCoy, whom she met in a recording studio in New York,^[21] breaking up in December 2008;^[104] Relient K frontman Matt Thiessen, with whom she worked on her album Teenage Dream^[105] and British comedian Russell Brand.

Perry first met Brand in the summer of 2009 when she filmed a cameo appearance for Brand's film Get Him to the Greek. Although the cameo ultimately did not make it into the final cut of the movie, Perry later noted that the "scene called for me to make out with him...And on the way down the stairs after the scene, I was hopping like a bunny. I hop like a bunny when I'm happy".^[106][107] Perry and Brand began dating after meeting again several months later in September 2009 at the 2009 MTV Video Music Awards, where Brand, as host, remarked, "Katy Perry didn't win an award and she's staying at the same hotel as me, so she's gonna need a shoulder to cry on. So in a way, I'm the real winner tonight."^[108] The couple became engaged in December 2009 while vacationing in India.^{[109][110][111]} At the time, Perry stated that she had plans to take dual British citizenship. "One of the first things I'll do is apply for dual citizenship. I'm not too sure if I have to take a test as I've not had time to look into it. But England is like my second home".^[112] In an August 2010 interview with Rolling Stone, Perry also noted that, "I am sensitive to Russell taking the Lord's name in vain and to Lady Gaga putting a rosary in her mouth. I think when you put sex and spirituality in the same bottle and shake it up, bad things happen."^{[113][114][115]} Perry and Brand married on October 23, 2010, in a traditional Hindu ceremony near the Ranthambhore tiger sanctuary in Rajasthan, India, the same location where Brand proposed.^[116][117]

After 14 months of marriage, Brand filed for divorce from Perry on December 30, 2011, in Los Angeles, citing irreconcilable differences.^[118][119] The announcement of the divorce followed media speculation that the couple was having marital problems, including an Us Weekly report that they had got into a "massive fight" and spent Christmas 2011 on opposite sides of the globe, with Perry in Hawaii and Brand in London, both without their wedding rings.^[120][121] After Perry and Brand reached an agreement on financial issues, a judge granted the divorce request in February 2012; however the divorce will not become effective until July 2012, as California law requires a six-month interval from the initial filing.^[122]

Discography[link]

• Katy Hudson (2001)
• One of the Boys (2008)
• Teenage Dream (2010)

Tours[link]

Filmography[link]

Awards and nominations[link]

References[link]