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We present a detailed study of the generalized hypergeometric systemintroduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) inthe context of toric geometry. GKZ systems arise naturally in the moduli theoryof Calabi-Yau toric varieties, and play an important role in applications ofthe mirror symmetry. We find that the Gr\"obner basis for the so-called toricideal determines a finite set of differential operators for the local solutionsof the GKZ system. At the special point called the large radius limit, we finda close relationship between the principal parts of the operators in the GKZsystem and the intersection ring of a toric variety. As applications, weanalyze general three dimensional hypersurfaces of Fermat and non-Fermat typeswith Hodge numbers up to $h^{1,1}=3$. We also find and analyze several nonLandau-Ginzburg models which are related to singular models.Comment: 55 pages, 3 Postscript figures, harvma

GKZ-Generalized hypergeometric systems in mirror symmetry of Calabi-Yau hypersurfaces