http://swrc.ontoware.org/ontology#UnrefereedArticle
Hodge Number of Cohomology of Local Systems on the Complement of Hyperplanes in $\Bbb P^3$
en
Hodge structure
cohomology of local system
Kawahara Yukihito
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.
Journal of mathematical sciences, the University of Tokyo
8
2
177-199
2001
13405705
AA11021653
application/pdf
415
Graduate School of Mathematical Sciences, The University of Tokyo