Big Line Bundles
A line bundle is big if it is of maximal Iitaka dimension, that is, if its Iitaka dimension is equal to the dimension of the underlying variety. Bigness is a birational invariant: If f : Y → X is a birational morphism of varieties, and if L is a big line bundle on X, then f*L is a big line bundle on Y.
All ample line bundles are big.
Big line bundles need not determine birational isomorphisms of X with its image. For example, if C is a curve of genus 2, then the canonical bundle KC is big, but it determines a two-to-one covering, a morphism C to its image as canonical curve, which here is a rational normal curve.
Read more about this topic: Iitaka Dimension
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