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.
Keywords: hypersphere arrangements, twisted cohomology, Gauss-Manin connection
@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}, pages = {977--995}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {4}, year = {2003}, doi = {10.5802/aif.1970}, mrnumber = {2033506}, zbl = {1087.32013}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1970/} }
TY - JOUR TI - Gauss-Manin connections of Schläfli type for hypersphere arrangements JO - Annales de l'Institut Fourier PY - 2003 DA - 2003/// SP - 977 EP - 995 VL - 53 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1970/ UR - https://www.ams.org/mathscinet-getitem?mr=2033506 UR - https://zbmath.org/?q=an%3A1087.32013 UR - https://doi.org/10.5802/aif.1970 DO - 10.5802/aif.1970 LA - en ID - AIF_2003__53_4_977_0 ER -
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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