Cohomology of the Orlik-Solomon 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 Orlik-Solomon algebra and cohomology of local systems are given. The methods are based on Vinberg-Kac classification of generalized Cartan matrices and study of pencils of algebraic curves defined by mentioned positive dimensional components.

arXiv commentlatex, 28 p

References in corpus (1)

• Geometry of cohomology support loci for local systems I

Cited by in corpus (10)

• Topology and geometry of cohomology jump loci
• Fundamental groups of line arrangements: Enumerative aspects
• The Milnor fibration of a hyperplane arrangement: from modular resonance to algebraic monodromy
• Resonance, linear syzygies, Chen groups, and the Bernstein-Gelfand-Gelfand correspondence
• On the monodromy action on Milnor fibers of graphic arrangements
• Fundamental groups, Alexander invariants, and cohomology jumping loci
• Homotopy types of complements of 2-arrangements in R^4
• Chen ranks and resonance
• Around the tangent cone theorem
• Efficient computation of resonance varieties via Grassmannians