# 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

## Access Full Article

top## Abstract

top## How to cite

topAomoto, 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

top- K. Aomoto, Configurations and invariant Gauss-Manin connections of integrals I, Tokyo J. of Math. 5 (1982), 249-287 Zbl0576.32017MR688126
- K. Aomoto, Errata to "Configurations and invariant Gauss-Manin connections of integrals. I", Tokyo J. of Math 22 (1999), 511-512 Zbl0941.32008MR1727748
- K. Aomoto, Hyperlogarithmic expansion and the volume of a hyperbolic Simplex, Partial Differential Equations 27 (1992), 9-21, Banach Center Publications Zbl0797.33008
- K. Aomoto, M. Kita, P. Orlik, H. Terao, Twisted de Rham cohomology groups of logarithmic forms, Adv. in Math 128 (1997), 119-152 Zbl0905.14010MR1451421
- D.C. Cohen, P. Orlik, Gauss-Manin connections for arrangements, II nonresonant weights, (2002) Zbl1078.32018MR2141645
- H. Horiuchi, H. Terao, The Poincaré series of the algebra of rational functions which are regular outside hyperplanes, (2002) Zbl1084.13501MR1994536
- Yi Hu, On the homology of complements of arrangements of subspaces and spheres, Proc. Amer. Math. Soc 122 (1994), 285-290 Zbl0810.57017MR1204377
- P. Orlik, H. Terao, Arrangements and Hypergeometric Integrals, MSJ memoirs (2001) Zbl0980.32010MR1814008
- P. Orlik, H. Terao, Commutative algebras for arrangements, Nagoya Math. J 134 (1994), 65-73 Zbl0801.05019MR1280653
- F. Pham, Introduction à l'Etude Topologique des Singularités de Landau, (1967), Gauthiers Villars Zbl0157.27503MR229263
- C. Sabbah, On the comparison theorem for elementary irregular $\mathcal{D}$-modules, Nagoya Math. J 141 (1996), 107-124 Zbl0858.32013MR1383794
- 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
- H. Terao, Algebras generated by reciprocals of linear forms, J. of Algebra 250 (2002), 549-558 Zbl1049.13011MR1899865
- K. Yoshida, Hypergeometric Functions, (1997), Vieweg Verlag Zbl0889.33008
- K. Aomoto, Vanishing of certain 1-form attached to a configuration, Tokyo J. of Math 9 (1986), 453-455 MR875200
- K. Aomoto, Configurations and invariant Gauss-Manin connections of integrals. II., Tokyo J. of Math. 6 (1983), 1-24 Zbl0576.32017MR707836

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.