Hodge Number of Cohomology of Local Systems on the Complement of Hyperplanes in $\Bbb P^3$

スポンサーリンク

概要

• 論文の詳細を見る

• The cohomology of the local system on the complement of hyperplanes has a Hodge structure as the $α$-invariant cohomology of a Kummer covering ramified along their hyperplanes for a generic character $α$. In this paper we study the case of arrangements of hyperplanes in the three dimensional complex projective space. We construct a resolution for an arrangement of hyperplanes and compute its Chow group. By computing the first Chern class of logarithmic 1-forms, we can obtain the Euler characteristic and the Hodge numbers of cohomology of local systems using the intersection set of the arrangement of hyperplanes and binomial coefficients.

• 東京大学の論文

著者

• Kawahara Yukihito

  Department Of Mathematics Tokyo Metropolitan University

• Kawahara Yukihito

  Department Of Mathematical Sciences University Of Tokyo

関連論文

• Hodge Number of Cohomology of Local Systems on the Complement of Hyperplanes in $\Bbb P^3$
• The mixed Hodge structure on the fundamental grop of the fiber type-2-arrangement

スポンサーリンク