Global division of cohomology classes via injectivity

Details Global division of cohomology classes via injectivity Global division of cohomology classes via injectivity

2007-12-19

arxiv.org/abs/0712.3186v2

Mathematics

Algebraic Geometry

10 pages; dedication included, and minor corrections made; to appear in the Michigan Math. J. volume in honor of Mel Hochster'

Scientific paper

We note that the vanishing and injectivity theorems of Koll\'ar and Esnault-Viehweg can be used to give a quick algebraic proof of a strengthening of the Ein-Lazarsfeld Skoda-type division theorem for global sections of adjoint line bundles vanishing along suitable multiplier ideal sheaves, and to extend it to higher cohomology classes as well. For global sections, this is also a slightly more general statement of the algebraic translation of an analytic result of Siu. Along the way we write down an injectivity statement for multiplier ideals, and its standard consequences.

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