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Advances in High Energy Physics
Volume 2011, Article ID 152749, 15 pages
http://dx.doi.org/10.1155/2011/152749
Review Article

Computational Tools for Cohomology of Toric Varieties

Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München, Germany

Received 15 April 2011; Accepted 27 June 2011

Academic Editor: André Lukas

Copyright © 2011 Ralph Blumenhagen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 package cohomCalg, its utility is highlighted on a new target space dual pair of ( 0 , 2 ) heterotic string models.