Non-vanishing of the twisted cohomology on the complement of hypersurfaces
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Abstract:
Generically, the cohomology with coefficients in a local system of rank one on the complement in $\mathbb {P}^n$ of the union of a finite number of hypersurfaces vanishes except in the highest dimension. We study the non-generic case, in which the cohomology in other dimensions does not vanish. When the hypersurfaces are hyperplanes, many examples of this kind are known. In this paper, we consider the case in which the hypersurfaces need not be hyperplanes. We prove that the hypersurfaces given by some particular linear systems have non-vanishing local system cohomologies.References
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Additional Information
- Yukihito Kawahara
- Affiliation: Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan
- Email: kawahara@z2.keio.jp
- Received by editor(s): February 26, 2006
- Received by editor(s) in revised form: May 7, 2007
- Published electronically: February 15, 2008
- Communicated by: Ted Chinburg
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1967-1975
- MSC (2000): Primary 14F40; Secondary 14C20, 32S22
- DOI: https://doi.org/10.1090/S0002-9939-08-09224-1
- MathSciNet review: 2383503