Cohomology of the OrlikSolomon algebras and local systems
Abstract
The paper provides a combinatorial method to decide when the space of local systems with non vanishing first cohomology on the complement to an arrangement of lines in a complex projective plane has as an irreducible component a subgroup of positive dimension. Partial classification of arrangements having such a component of positive dimension and a comparison theorem for cohomology of OrlikSolomon algebra and cohomology of local systems are given. The methods are based on VinbergKac classification of generalized Cartan matrices and study of pencils of algebraic curves defined by mentioned positive dimensional components.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1998
 DOI:
 10.48550/arXiv.math/9806137
 arXiv:
 arXiv:math/9806137
 Bibcode:
 1998math......6137L
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Mathematical Physics;
 Mathematical Physics
 EPrint:
 latex, 28 p