Cohomology of line bundles: A computational algorithm

2010/10/01 by Ralph Blumenhagen, Benjamin Jurke, Thorsten Rahn +1 · 9 citations
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.1063/1.3501132

Abstract

We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and type IIB/F-theory compactifications, where the manifolds of interest are complete intersections of hypersurfaces in toric varieties supporting additional vector bundles.

Cited by

• Cohomology Chambers on Complex Surfaces and Elliptically Fibered Calabi-Yau Three-folds
• Spectral Covers, Integrality Conditions, and Heterotic/F-theory Duality
• Chow groups, Deligne cohomology and massless matter in F-theory
• On genus one fibered Calabi-Yau threefolds with 5-sections
• Calabi-Yau compactifications of non-supersymmetric heterotic string\n theory
• Assisted Fibre Inflation in Perturbative LVS
• Combinatorics in N = 1 Heterotic Vacua
• Strongly coupled phases of N=1 S-duality
• Elusive Worldsheet Instantons in Heterotic String Compactifications

Related

• Cohomology Chambers on Complex Surfaces and Elliptically Fibered Calabi-Yau Three-folds
• Cohomology of line bundles on a toric variety and constructible sheaves on its polytope
• Computing the cohomology of line bundles on the incidence correspondence and related invariants
• Displaying the cohomology of toric line bundles
• Immaculate line bundles on toric varieties