Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-03T05:09:49.931Z Has data issue: false hasContentIssue false
  • English
  • Français

Hodge structure on twisted cohomologies and twisted Riemann inequalities I

Published online by Cambridge University Press:  22 January 2016

Masaki Hanamura  and
Masaaki Yoshida
Masaki Hanamura
Affiliation:
Graduate School of Mathematics, Kyushu University 33, Fukuoka 812-8581, Japan
Masaaki Yoshida
Affiliation:
Graduate School of Mathematics, Kyushu University 33, Fukuoka 812-8581, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show the twisted cohomology on has a natural polarized Hodge structure and hence derive the analogues of Riemann’s equality and inequailty.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 154 , 1999 , pp. 123 - 139
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

References

[AK] Aomoto, K. and Kita, M., Hypergeometric functions, Springer-Verlag, Tokyo, 1994, (Japanese).Google Scholar
[CM] Cho, K. and Matsumoto, K., Intersection theory for twisted cohomologies and twisted Riemann’s period relation I, Nagoya Math. J., 139 (1995), 67–86.CrossRefGoogle Scholar
[CY] Cho, K. and Yoshida, M., Comparison of (co)homologies of branched covering spaces and twisted ones of basespaces, Kyushu J. Math., 45 (1994), 111–122.Google Scholar
[G] Griffiths, Ph., ed., Topics in Transcendental Algebraic Geometry, Princeton Univ. Press, 1984.CrossRefGoogle Scholar
[KY] Kita, M. and Yoshida, M., Intersection theory for twisted cycles, Math. Nachr., 166 (1994), 287–304.CrossRefGoogle Scholar
[M1] Matsumoto, K., Quadratic identities for hypergeometric series of type (k, l), Kyushu J. of Math., 48 (1994), 335–345.CrossRefGoogle Scholar
[M2] Matsumoto, K., Intersection numbers for logarithmic k-forms, Preprint (1996).Google Scholar
[Y] Yoshida, M., Hypergeometric Functions, My Love, Vieweg, Wiesbaden, 1997.CrossRefGoogle Scholar
[Zuc] Zucker, S., Hodge theory with degenerating coefficients: L2 cohomology in the Poincaré metric, Ann. of Math., 109 (1979), 415–176.CrossRefGoogle Scholar