- published: 24 Oct 2013
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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 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.
Given a morphism , any vector bundle on Y, or more generally any sheaf in modules, e.g. 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
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.
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I´ll stand up and fight.
To the sound of screaming guitars.
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I´m starting to play.
Noone can stop my metal crusade.
Deep in my heart there's no doubt,
raise my fist scream and shout.
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in this moment you'll see.
I'm a rocker and lone,
not just one of those clones.
Keeper of the Flame
Gonna break the chains and run away.
Keeper of the Flame
Hold your head up high no matter what they say.
So stare at me,
I laugh you see.
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I'll never leave,
roll up your sleeve.
In a seconds time, you crossed my line.