Gauss-Manin connections of Schläfli type for hypersphere arrangements

Kazuhiko Aomoto[1]

  • [1] University of Nagoya, Department of Mathematics, Nagoya (Japon)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 4, page 977-995
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Aomoto, Kazuhiko. "Gauss-Manin connections of Schläfli type for hypersphere arrangements." Annales de l’institut Fourier 53.4 (2003): 977-995. <http://eudml.org/doc/116071>.

@article{Aomoto2003,
abstract = {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.},
affiliation = {University of Nagoya, Department of Mathematics, Nagoya (Japon)},
author = {Aomoto, Kazuhiko},
journal = {Annales de l’institut Fourier},
keywords = {hypersphere arrangements; twisted cohomology; Gauss-Manin connection},
language = {eng},
number = {4},
pages = {977-995},
publisher = {Association des Annales de l'Institut Fourier},
title = {Gauss-Manin connections of Schläfli type for hypersphere arrangements},
url = {http://eudml.org/doc/116071},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Aomoto, Kazuhiko
TI - Gauss-Manin connections of Schläfli type for hypersphere arrangements
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 4
SP - 977
EP - 995
AB - 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.
LA - eng
KW - hypersphere arrangements; twisted cohomology; Gauss-Manin connection
UR - http://eudml.org/doc/116071
ER -

References

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  3. K. Aomoto, Hyperlogarithmic expansion and the volume of a hyperbolic Simplex, Partial Differential Equations 27 (1992), 9-21, Banach Center Publications Zbl0797.33008
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  10. F. Pham, Introduction à l'Etude Topologique des Singularités de Landau, (1967), Gauthiers Villars Zbl0157.27503MR229263
  11. C. Sabbah, On the comparison theorem for elementary irregular 𝒟 -modules, Nagoya Math. J 141 (1996), 107-124 Zbl0858.32013MR1383794
  12. H. Terao, Moduli space of combinatorially equivalent arrangements of hyperplanes and logarithmic Gauss-Manin connections, Topology and its Appl. 118 (2002), 255-274 Zbl1020.52020MR1877728
  13. H. Terao, Algebras generated by reciprocals of linear forms, J. of Algebra 250 (2002), 549-558 Zbl1049.13011MR1899865
  14. K. Yoshida, Hypergeometric Functions, (1997), Vieweg Verlag Zbl0889.33008
  15. K. Aomoto, Vanishing of certain 1-form attached to a configuration, Tokyo J. of Math 9 (1986), 453-455 MR875200
  16. K. Aomoto, Configurations and invariant Gauss-Manin connections of integrals. II., Tokyo J. of Math. 6 (1983), 1-24 Zbl0576.32017MR707836

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