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Cohomology of toric line bundles via simplicial Alexander duality. (English) Zbl 1315.55010
Summary: 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 et al. [ibid. 51, No. 10, 103525, 15 p. (2010; Zbl 1314.55012)]. 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 [ibid. 51, No. 10, 103520, 11 p. (2010; Zbl 1314.55013)], 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 [H. Roschy and T. Rahn, loc. cit.].{
©2011 American Institute of Physics}

55R20 Spectral sequences and homology of fiber spaces in algebraic topology
55U10 Simplicial sets and complexes in algebraic topology
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
05E45 Combinatorial aspects of simplicial complexes
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
Full Text: DOI arXiv
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