Computing Cohomology on Toric Varieties
arXiv:1109.1571
Abstract
In these notes a recently developed technique for the computation of line bundle-valued sheaf cohomology group dimensions on toric varieties is reviewed. The key result is a vanishing theorem for the contributing components which depends on the structure of the Stanley-Reisner ideal generators. A particular focus is placed on the (simplicial) Alexander duality that provides a central tool for the two known proofs of the algorithm.
10 pages; contribution to the proceedings of the String Math 2011 conference, UPenn, Philadelphia, June 6-11, 2011