Computational Tools for Cohomology of Toric Varieties

Abstract

In this review, novel non-standard 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.

17 pages, 4 tables; prepared for the special issue "Computational Algebraic Geometry in String and Gauge Theory" of Advances in High Energy Physics, cohomCalg implementation available at http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg/

References in corpus (3)

• Cohomology of Line Bundles: A Computational Algorithm
• On the computation of non-perturbative effective potentials in the string theory landscape -- IIB/F-theory perspective
• Cohomology of Line Bundles: Proof of the Algorithm

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• Stabilising all Kähler moduli in perturbative LVS
• Systematics of perturbatively flat flux vacua
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• Global Embedding of Fibre Inflation in Perturbative LVS
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• Target Space Dualities of Heterotic Grand Unified Theories
• Generating Functions for Line Bundle Cohomology Dimensions on Complex Projective Varieties
• A Database of Calabi-Yau Orientifolds and the Size of D3-Tadpoles
• Divisor topologies of CICY 3-folds and their applications to phenomenology
• Computing Cohomology on Toric Varieties