Hyperplane arrangements, M-tame polynomials and twisted cohomology

2002/12/18 by Alexandru Dimca, A. Dimca, Dimca, A.
Mathematics · #14D05 #32S22 #52C35 #55N25 #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.AG #math.AT #msc:14D05 #msc:32S22 #msc:52C35 #msc:55N25

paper · pdf · doi:10.48550/arxiv.math/0212248

14 pages

arxiv created 2002/12/18 · openalex publication_date 2002/12/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new relation between a class of complex polynomials with a good behavior at infinity studied by A. Némethi and A. Zaharia and the cohomology groups of affine complex hyperplane arrangement complements with rank one local system coefficients is introduced and explored. This approach gives in particular new upper-bounds for the dimension of the twisted cohomology groups of line arrangement complements in the complex affine plane.

Related

• Minimality of hyperplane arrangements and basis of local system cohomology
• Cohomology of hyperplane complements with group ring coefficients
• Length and multiplicity of the local cohomology with support in a hyperplane arrangement
• Length and decomposition of the cohomology of the complement to a hyperplane arrangement
• Hodge spectrum of hyperplane arrangements