Resonant hypergeometric series

Bernd Sturmfels

UC Berkeley

May 7,
refreshments at 3:45pm


We present a basis of logarithmic series solutions at a point of maximal degeneracy to the Gelfand-Kapranov-Zelevinsky hypergeometric equations. These differential equations were studied by Batyrev, Hosono-Lian-Yau and Stienstra in the context of toric mirror symmetry. Our new construction is combinatorial and gives an explicit formula for the terms of such a series. Main ingredients are volumes of convex polytopes and shellings of triangulations. This talk is based on the material in Section 3.6 of the forthcoming book "Gr\"obner Deformations of Hypergeometric Differential Equations" (with M.~Saito and N.~Takayama). The current draft of our book is available at my homepage.

Speaker's Contact Info: bernd(at-sign)

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