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- W2950819480 abstract "The Gamma-series of Gel'fand-Kapranov-Zelevinsky are adapted so that they give solutions for certain resonant systems of GKZ hypergeometric differential equations. For this some complex parameters in the Gamma-series are replaced by nilpotent elements from a ring $R_{A,T}$. The adapted Gamma-series is a function $Psi$ with values in the finite dimensional vector space $R_{A,T}otimes C$. Applications of these results in the context of toric Mirror Symmetry are described. Building on work of Batyrev we show that the relative cohomology module of a certain hypersurface in a torus is a GKZ hypergeometric $D$-module which over an appropriate domain is isomorphic to the trivial $D$-module $R_{A,T}otimes O_T$, where $O_T$ is the sheaf of holomorphic functions on this domain. The isomorphism is explicitly given by adapted Gamma-series. As a result one finds the periods of a holomorphic differential form of degree $d$ on a $d$-dimensional Calabi-Yau manifold, needed for the B-model side input to Mirror Symmetry. Relating our work with that of Batyrev and Borisov we interpret the ring $cR_{sA,gT}$ as the cohomology ring of a toric variety and a certain principal ideal in it as a subring of the Chow ring of a Calabi-Yau complete intersection. This interpretation takes place on the A-model side of Mirror Symmetry." @default.
- W2950819480 created "2019-06-27" @default.
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- W2950819480 date "1997-11-03" @default.
- W2950819480 modified "2023-09-27" @default.
- W2950819480 title "Resonant Hypergeometric Systems and Mirror Symmetry" @default.
- W2950819480 hasPublicationYear "1997" @default.
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