Gauss-Manin connections of Schläfli type for hypersphere arrangements  [ Connexions de Gauss-Manin de type Schläfli pour des arrangements hypersphériques ]
Annales de l'Institut Fourier, Tome 53 (2003) no. 4, p. 977-995
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.
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.
DOI : https://doi.org/10.5802/aif.1970
Classification:  32S22,  32S40,  33C70,  39B32
Mots clés: arrangements hypersphériques, cohomologie des n{\oe}uds, connexion de Gauss-Manin
@article{AIF_2003__53_4_977_0,
     author = {Aomoto, Kazuhiko},
     title = {Gauss-Manin connections of Schl\"afli type for hypersphere arrangements},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {4},
     year = {2003},
     pages = {977-995},
     doi = {10.5802/aif.1970},
     zbl = {1087.32013},
     mrnumber = {2033506},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2003__53_4_977_0}
}
Aomoto, Kazuhiko. Gauss-Manin connections of Schläfli type for hypersphere arrangements. Annales de l'Institut Fourier, Tome 53 (2003) no. 4, pp. 977-995. doi : 10.5802/aif.1970. http://www.numdam.org/item/AIF_2003__53_4_977_0/

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