ample line bundle

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  • Info 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 M into projective space. more...
  • Koizumi's theorem states the third power of an ample line bundle is normally generated.
  • This construction builds a projective algebraic variety together with a very ample line bundle whose homogeneous coordinate ring is the original ring.
  • In particular, every ample line bundle is nef.
  • The Mumford-Kempf theorem states that the fourth power of an ample line bundle is quadratically presented.
  • The existence of some ample line bundle on X is equivalent to X being a projective variety, so a Fano variety is always projective.
  • These vector bundles arise as the zeroth direct images of the adjoint of an ample line bundle over the fibration.
  • To decide in practice when a Cartier divisor D corresponds to an ample line bundle, there are some geometric criteria.
  • In algebraic geometry, a Seshadri constant is an invariant of an ample line bundle L at a point P on an algebraic variety.
  • In algebraic geometry, given an ample line bundle L on a compact complex manifold X, Matsusaka's big theorem gives an integer m such that the tensor power L^m is very ample.
  • Looking at the issue from the point of view of a given very ample line bundle giving rise to the projective embedding of V, such a line bundle (invertible sheaf) is said to be normally generated if V as embedded is projectively normal.