DOCUMENTA MATHEMATICA, Vol. 16 (2011), 209-251

Markus Perling

Divisorial Cohomology Vanishing on Toric Varieties

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 Iitaka dimension. Finally, we give a new criterion for divisorial sheaves for being maximal Cohen-Macaulay.

2010 Mathematics Subject Classification: 13C14, 14B15, 14M25

Keywords and Phrases: toric varieties, cohomology, local cohomology, Weil divisors, Maximal Cohen-Macaualy modules

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