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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