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/

References in corpus (4)

• Les Houches Lectures on Constructing String Vacua
• Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds
• The Geometer's Toolkit to String Compactifications
• Cohomology of Line Bundles: Proof of the Algorithm

Cited by in corpus (6)

• Toric Construction of Global F-Theory GUTs
• A Note on Poly-Instanton Effects in Type IIB Orientifolds on Calabi-Yau Threefolds
• Cohomology of Line Bundles: Proof of the Algorithm
• Elusive Worldsheet Instantons in Heterotic String Compactifications
• Strongly coupled phases of $\mathcal{N}=1$ S-duality
• Combinatorics in N = 1 Heterotic Vacua