Hodge Number of Cohomology of Local Systems on the Complement of Hyperplanes in $\Bbb P^3$
Vol. 8 (2001), No. 2, Page 177--199.
Kawahara, Yukihito
Hodge Number of Cohomology of Local Systems on the Complement of Hyperplanes in $\Bbb P^3$
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Abstract:
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.
Keywords: Hodge structure, cohomology of local system, arrangement of hyperplanes, Kummer covering, Euler characteristic, blowing up, logarithmic form, Chow group, Chern class
Mathematics Subject Classification (1991): Primary 14E22, 52B30; Secondary 14C30, 14E20, 14J30, 58A14
Mathematical Reviews Number: MR1837160
Received: 2000-03-02
