Geodesic
Divisorial cohomology vanishing on toric varieties
Documenta mathematica, Tome 16 (2011), pp. 209-251
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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.
DOI : 10.4171/dm/331
Classification : 13C14, 14B15, 14M25
Mots-clés : toric varieties, local cohomology, cohomology, Weil divisors, maximal Cohen-macaualy modules 
@article{10_4171_dm_331,
     author = {Markus Perling},
     title = {Divisorial cohomology vanishing on toric varieties},
     journal = {Documenta mathematica},
     pages = {209--251},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/331},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/331/}
}
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Markus Perling. Divisorial cohomology vanishing on toric varieties. Documenta mathematica, Tome 16 (2011), pp. 209-251. doi: 10.4171/dm/331

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