Minimality of hyperplane arrangements and basis of local system cohomology

  • Masahiko Yoshinaga

    Kyoto University, Japan
Minimality of hyperplane arrangements  and basis of local system cohomology cover
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Abstract

The purpose of this paper is applying minimality of hyperplane arrangements to local system cohomology groups. It is well known that twisted cohomology groups with coefficients in a generic rank one local system vanish except in the top degree, and bounded chambers form a basis of the remaining cohomology group. We determine precisely when this phenomenon happens for two-dimensional arrangements.