Cohomology of toric line bundles via simplicial Alexander duality

Details Cohomology of toric line bundles via simplicial Alexander duality Cohomology of toric line bundles via simplicial Alexander duality

2010-06-04

arxiv.org/abs/1006.0780v2

Mathematics

Algebraic Geometry

9 pages. Theorem 1.1 and Corollary 1.2 improved; Abstract and Introduction modified; References updated. To appear in Journal

Scientific paper

We give a rigorous mathematical proof for the validity of the toric sheaf cohomology algorithm conjectured in the recent paper by R. Blumenhagen, B. Jurke, T. Rahn, and H. Roschy (arXiv:1003.5217). We actually prove not only the original algorithm but also a speed-up version of it. Our proof is independent from (in fact appeared earlier on the arXiv than) the proof by H. Roschy and T. Rahn (arXiv:1006.2392), and has several advantages such as being shorter and cleaner and can also settle the additional conjecture on "Serre duality for Betti numbers" which was raised but unresolved in arXiv:1006.2392.

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