Cohomology of Line Bundles: Proof of the Algorithm

@article{Roschy2010CohomologyOL,
  title={Cohomology of Line Bundles: Proof of the Algorithm},
  author={Helmut Roschy and Thorsten Rahn},
  journal={arXiv: High Energy Physics - Theory},
  year={2010}
}
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 kind of Serre duality for combinatorial Betti numbers that we observed when computing examples. 
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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
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We give a rigorous mathematical proof for the validity of the toric sheaf cohomology algorithm conjectured in the recent paper by Blumenhagen, Jurke, Rahn, and Roschy (arXiv:1003.5217). We actually
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