Computational Tools for Cohomology of Toric Varieties

Abstract

Novel nonstandard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational algorithm for the determination of the dimension of line-bundle-valued cohomology groups on toric varieties. Applications to the computation of chiral massless matter spectra in string compactifications are discussed, and using the software packagecohomCalg, its utility is highlighted on a new target space dual pair of(0,2)heterotic string models.