Divisorial Cohomology Vanishing on Toric Varieties

Details Divisorial Cohomology Vanishing on Toric Varieties Divisorial Cohomology Vanishing on Toric Varieties

2007-11-29

arxiv.org/abs/0711.4836v2

Documenta Math. 16, 209-251, 2011

Mathematics

Algebraic Geometry

35 pages, 4 figures, requires packages ams*, enumerate, graphicx, xy, rewritten version

Scientific paper

This work discusses combinatorial and arithmetic aspects of cohomology vanishing for divisorial sheaves on toric varieties. We obtain a refined variant of the Kawamata-Viehweg theorem which is slightly stronger. Moreover, we prove a new vanishing theorem related to divisors whose inverse is nef and has small Kodaira dimension. Finally, we give a new criterion for divisorial sheaves for being maximal Cohen-Macaulay.

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