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

Full text: dvi.gz 84 k, dvi 201 k, ps.gz 432 k, pdf 416 k.

Home Page of DOCUMENTA MATHEMATICA