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Intersection theory for twisted cohomologies and twisted Riemann’s period relations I

Published online by Cambridge University Press:  22 January 2016

Koji Cho  and
Keiji Matsumoto
Koji Cho
Affiliation:
Graduate School of Mathematics, Kyushu University, Hakozaki, Higashi-ku Fukuoka 812, Japan
Keiji Matsumoto
Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, Kagamiyama, Higashi-Hiroshima 739, Japan
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The beta function B(α, β) is defined by the following integral

where arg , and the gamma function Γ(β) by

where arg .

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 139 , September 1995 , pp. 67 - 86
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

References

[Aom1] Aomoto, K., On vanishing of cohomology attached to certain many valued mero-morphic functions, J. Math. Soc. Japan, 27 (1975), 248–255.CrossRefGoogle Scholar
[Aom2] Aomoto, K., On the structure of intergrals of power product of linear functions, Sci. Papers College of General Ed, Univ. of Tokyo, 27 (1977), 49–61.Google Scholar
[Cho1] Cho, K., Intersection theory for twisted cohomologies and twisted Riemann’s period relations II-On Riemann srufaces, preprint.Google Scholar
[Cho2] Cho, K., Intersectin theory for twisted cohomologies and twisted Riemann’s period relations III-On P , preprint.Google Scholar
[CY] Cho, K. and Yoshida, M., Comparison of (co)homologies of branched covering spaces and twisted ones of basespaces I, Kyushu J. Math., 48 (1994), 111–122.CrossRefGoogle Scholar
[Dell] Deligne, P., Equations différentielles à points singuliers réguliers, Lect. Notes in Math., 163, Springer, 1970.Google Scholar
[Del2] Deligne, P., Théorie de Hodge II, Publ. Math., Inst. Hautes Etud. Sci., 40 (1972), 5–57.Google Scholar
[EV1] Esnault, H. and Viehweg, E., Logarithmic De Rham complexes and vanishing theorems, Invent. Math., 86 (1986), 161–194.Google Scholar
[EV2] Esnault, H. and Viehweg, E., Lectures on Vanishing Theorems, Birkhäuser, 1992.Google Scholar
[ESV] Esnault, H., Schechtman, V. and Viehweg, E., Cohomology of local systems on the complement of hyperplanes, Invent, Math., 109 (1992), 557–561.Google Scholar
[For] Forster, O., Lectures on Riemann Surfaces, GTM 81, Springer, 1977.Google Scholar
[GH] Griffiths, P. and Harirs, J., Principles of Algebraic Geometry, John Wiley & Sons, Inc., 1978.Google Scholar
[IK1] Iwasaki, K. and Kita, M., Exterior power structure of the twisted de Rham cohomology of the complement of real Veromese arrangements, to appear in J. Math. Pures et Appl.Google Scholar
[IK2] Iwasaki, K. and Kita, M., Twisted homology of the configuration space of w-points with application to hypergeometric functions, preprint UTMS 94–11, (1944).Google Scholar
[IKSY] Iwasaki, K. Kimura, H., Shimomura, S. and Yoshida, M., From Gauss to Painlevé, Vieweg, 1991.CrossRefGoogle Scholar
[Kit] Kita, M., On the hypergeometric functions in several variables II-On the Wronskian of the hypergeometric functions of type (n + 1, m + 1)−, J. Math. Soci. Japan, 45 (1993), 645–669.Google Scholar
[KM] Kita, M. and Matsumoto, K., Duality for hypergeometric furctions and inrariant Gauss-Manin systems preprint.Google Scholar
[KN] Kita, M. and Noumi, M., On the structure of cohomology groups attached to integrals of certain many valued analytic functions, Japan. J. Math., 9 (1983), 113–157.CrossRefGoogle Scholar
[KY1, 2] Kita, M. and Yoshida, M., Intersection theory for twisted cycles I, II, Math. Nachrichten, 166 (1994), 287–304, 168 (1994), 171–190.Google Scholar
[SY] Sasaki, T. and Yoshida, M., Tensor Products of Linear Differential Equations II – New formulae for the hypergeometric functions –, Funkcialaj Ekvacioj, 33 (1990), 527–549.Google Scholar
[Yos] Yoshida, M., Fuchsian Differential Equations, Vieweg, 1987.Google Scholar