Resonant hypergeometric series
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)math.berkeley.edu
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