Computing Cohomology on Toric Varieties

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.