Hypergeometric integrals associated with hypersphere arrangements and Cayley-Menger determinants

2017/09/27 by Aomoto, Kazuhiko, Machida, Yoshinori
#14F40 #14H70 (Secondary) #33C70 (Primary) #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1709.09329

Abstract

The n-dimensional hypergeometric integrals associated with a hypersphere arrangement are formulated by the pairing of n-dimensional twisted cohomology and its dual. Under the condition of general position there are stated some results which concern an explicit representation of the standard form by a special (NBC) basis of the twisted cohomology, the variational formula of the corresponding integral in terms of special invariant 1-forms written by Cayley-Menger minor determinants. Gauss-Manin connection is also formulated and is explicitly presented in two simplest cases.

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