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February 2020 Hypergeometric integrals associated with hypersphere arrangements and Cayley-Menger determinants
Kazuhiko AOMOTO, Yoshinori MACHIDA
Hokkaido Math. J. 49(1): 1-85 (February 2020). DOI: 10.14492/hokmj/1591085012

Abstract

The $n$-dimensional hypergeometric integrals associated with a hypersphere arrangement $S$ are formulated by the pairing of $n$-dimensional twisted cohomology $H_\nabla^n (X, \Omega^\cdot (*S))$ and its dual. Under the condition of general position we present an explicit representation of the standard form by a special (NBC) basis of the twisted cohomology (contiguity relation in positive direction), the variational formula of the corresponding integral in terms of special invariant $1$-forms $\theta_J$ written by Calyley-Menger minor determinants, and a connection relation of the unique twisted $n$-cycle identified with the unbounded chamber to a special basis of twisted $n$-cycles identified with bounded chambers. Gauss-Manin connections are formulated and are explicitly presented in two simplest cases. In the appendix contiguity relation in negative direction is presented in terms of Cayley-Menger determinants.

Citation

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Kazuhiko AOMOTO. Yoshinori MACHIDA. "Hypergeometric integrals associated with hypersphere arrangements and Cayley-Menger determinants." Hokkaido Math. J. 49 (1) 1 - 85, February 2020. https://doi.org/10.14492/hokmj/1591085012

Information

Published: February 2020
First available in Project Euclid: 2 June 2020

zbMATH: 07209520
MathSciNet: MR4105536
Digital Object Identifier: 10.14492/hokmj/1591085012

Subjects:
Primary: 14F40, 33C70
Secondary: 14H70

Rights: Copyright © 2020 Hokkaido University, Department of Mathematics

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Vol.49 • No. 1 • February 2020
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