Open Access
June 2015 Some problems of hypergeometric integrals associated with hypersphere arrangement
Kazuhiko Aomoto, Yoshinori Machida
Proc. Japan Acad. Ser. A Math. Sci. 91(6): 77-81 (June 2015). DOI: 10.3792/pjaa.91.77


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 there are stated some results and conjectures which concern a representation of the standard form by a special basis of the twisted cohomology, the variational formula of the corresponding integral in terms of special invariant 1-forms using Calyley-Menger minor determinants, 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. General conjectures are presented under a much weaker assumption.


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Kazuhiko Aomoto. Yoshinori Machida. "Some problems of hypergeometric integrals associated with hypersphere arrangement." Proc. Japan Acad. Ser. A Math. Sci. 91 (6) 77 - 81, June 2015.


Published: June 2015
First available in Project Euclid: 3 June 2015

zbMATH: 1325.14036
MathSciNet: MR3353092
Digital Object Identifier: 10.3792/pjaa.91.77

Primary: 14F40 , 33C70
Secondary: 14H70

Keywords: Cayley-Menger determinant , contiguity relation , Gauss-Manin connection , hypergeometric integral , hypersphere arrangement , twisted rational de Rham cohomology

Rights: Copyright © 2015 The Japan Academy

Vol.91 • No. 6 • June 2015
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