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Computational tools for cohomology of toric varieties. (English) Zbl 1234.81107
Summary: Novel nonstandard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational algorithm for the determination of the dimension of line-bundle-valued cohomology groups on toric varieties. Applications to the computation of chiral massless matter spectra in string compactifications are discussed, and using the software package cohomCalg, its utility is highlighted on a new target space dual pair of $$(0,2)$$ heterotic string models.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81V25 Other elementary particle theory in quantum theory 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies 81T80 Simulation and numerical modelling (quantum field theory) (MSC2010) 81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
##### Software:
cohomCalg; Macaulay2; PALP; SageMath; TOPCOM; ToricVectorBundles
Full Text:
##### References:
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