Cohomology of Line Bundles: A Computational Algorithm

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.

11 pages, 1 figure, 2 tables; v2: typos and references corrected; v3: proof-related statements updated, cohomCalg implementation available at http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg/

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• Phases of $N=2$ Theories In Two Dimensions
• Calabi-Yau Moduli Space, Mirror Manifolds and Spacetime Topology Change in String Theory
• Les Houches Lectures on Constructing String Vacua
• Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds
• Global F-theory Models: Instantons and Gauge Dynamics
• Resolving Singularities in (0,2) Models
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• Cohomology of Line Bundles: Applications
• Toric Geometry and Calabi-Yau Compactifications
• Cohomology of Line Bundles: Proof of the Algorithm
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