# Cohomology of line bundles: Applications

@article{Blumenhagen2012CohomologyOL, title={Cohomology of line bundles: Applications}, author={Ralph Blumenhagen and Benjamin Jurke and Thorsten Rahn and Helmut Roschy}, journal={Journal of Mathematical Physics}, year={2012}, volume={53}, pages={012302} }

Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued cohomology classes over toric varieties are presented. For the heterotic string, the prime examples are so-called monad constructions on Calabi-Yau manifolds. In the context of Type II orientifolds, one often needs to compute cohomology for line bundles on…

## 33 Citations

Computational Tools for Cohomology of Toric Varieties

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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.

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In these notes a recently developed technique for the computation of line bundle-valued sheaf cohomology group dimensions on toric varieties is reviewed. The key result is a vanishing theorem for the…

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We prove a formula for the Hodge numbers of square‐free divisors of Calabi‐Yau threefold hypersurfaces in toric varieties. Euclidean branes wrapping divisors affect the vacuum structure of Calabi‐Yau…

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We briefly review an algorithmic strategy to explore the landscape of heterotic E8×E8 vacua, in the context of compactifying smooth Calabi-Yau three-folds with vector bundles. The Calabi-Yau…

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