Computing Cohomology on Toric Varieties

Details Computing Cohomology on Toric Varieties Computing Cohomology on Toric Varieties

2011-09-07

arxiv.org/abs/1109.1571v1

Mathematics

Algebraic Geometry

10 pages; contribution to the proceedings of the String Math 2011 conference, UPenn, Philadelphia, June 6-11, 2011

Scientific paper

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.

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