Gauss-Manin connections of Schläfli type for hypersphere arrangements
Annales de l'Institut Fourier, Volume 53 (2003) no. 4, pp. 977-995.

The cohomological structure of hypersphere arragnements is given. The Gauss-Manin connections for related hypergeometrtic integrals are given in terms of invariant forms. They are used to get the explicit differential formula for the volume of a simplex whose faces are hyperspheres.

Nous donnons la structure cohomologique des arrangements hypersphériques. Les connexions de Gauss-Manin pour les intégrales hypergéométriques associées sont données en termes de formes invariantes. Elles sont utilisées pour obtenir la formule explicite du volume d'un simplexe dont les faces sont hypersphériques.

DOI: 10.5802/aif.1970
Classification: 32S22,  32S40,  33C70,  39B32
Keywords: hypersphere arrangements, twisted cohomology, Gauss-Manin connection
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     title = {Gauss-Manin connections of {Schl\"afli} type for hypersphere arrangements},
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Aomoto, Kazuhiko. Gauss-Manin connections of Schläfli type for hypersphere arrangements. Annales de l'Institut Fourier, Volume 53 (2003) no. 4, pp. 977-995. doi : 10.5802/aif.1970. https://aif.centre-mersenne.org/articles/10.5802/aif.1970/

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