Non-vanishing of the twisted cohomology on the complement of hypersurfaces

2005/06/22 by Yukihito Kawahara, Kawahara, Yukihito
Mathematics · #14C20 #14F40 #32S22 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT #msc:14C20 #msc:14F40 #msc:32S22

paper · pdf · doi:10.48550/arxiv.math/0506439

7 pages

arxiv created 2005/06/22 · arxiv updated 2009/12/01

Abstract

Under the generic situation, the cohomology with the coefficients in the local system on complements of hypersurfaces vanishes except in the highest dimension. Our problem is of when the local system cohomology does not vanish. In the case of arrangements of hyperplanes, many examples were founded. In this paper, we shall generalize their examples to hypersurfaces. We obtain that hypersurfaces given by some linear system have non-vanishing local system cohomologies.

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