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Cohomology of line bundles: Applications. (English) Zbl 1273.81180
Summary: 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 finite group action coset spaces, necessitating us to generalize our algorithm to this case. Moreover, we exemplify that the different terms in Batyrev’s formula and its generalizations can be given a one-to-one cohomological interpretation. Furthermore, we derive a combinatorial closed form expression for two Hodge numbers of a codimension two Calabi-Yau fourfold.{
©2012 American Institute of Physics}

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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