Cohomology of line bundles: A computational algorithm

@article{Blumenhagen2010CohomologyOL,
  title={Cohomology of line bundles: A computational algorithm},
  author={Ralph Blumenhagen and Benjamin Jurke and Thorsten Rahn and Helmut Roschy},
  journal={Journal of Mathematical Physics},
  year={2010},
  volume={51},
  pages={103525-103525}
}
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. 

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We present a proof of the algorithm for computing line bundle valued cohomology classes over toric varieties conjectured by R.~Blumenhagen, B.~Jurke and the authors (arXiv:1003.5217) and suggest a
Cohomology of line bundles: Applications
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
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