Abstract
We present a detailed study of the generalized hypergeometric system introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in the context of toric geometry. GKZ systems arise naturally in the moduli theory of Calabi-Yau toric varieties, and play an important role in applications of the mirror symmetry. We find that the Gröbner basis for the so-called toric ideal determines a finite set of differential operators for the local solutions of the GKZ system. At the special point called the large radius limit, we find a close relationship between the principal parts of the operators in the GKZ system and the intersection ring of a toric variety. As applications, we analyze general three dimensional hypersurfaces of Fermat and non-Fermat types with Hodge numbers up toh 1,1=3. We also find and analyze several non-Landau-Ginzburg models which are related to singular models.
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Communicated by R.H. Dijkgraaf
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Hosono, S., Lian, B.H. & Yau, S.T. GKZ-Generalized hypergeometric systems in mirror symmetry of Calabi-Yau hypersurfaces. Commun.Math. Phys. 182, 535–577 (1996). https://doi.org/10.1007/BF02506417
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DOI: https://doi.org/10.1007/BF02506417