Admissible local systems for a class of line arrangements

2008/01/23 by Shaheen Nazir, Nazir, Shaheen, Zahid Raza +1
Mathematics · #14C21 #14E05 (Secondary) #14F99 #32S22 (Primary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C21 #msc:14E05 #msc:14F99 #msc:32S22

paper · pdf · doi:10.48550/arxiv.0801.3512

9 pages, 2figures

arxiv created 2008/02/22 · arxiv updated 2009/12/01

Abstract

A rank one local system \LL on a smooth complex algebraic variety M is admissible roughly speaking if the dimension of the cohomology groups H^m(M,\LL) can be computed directly from the cohomology algebra H^*(M,\C). We say that a line arrangement \A is of type \CC_k if k ≥ 0 is the minimal number of lines in \A containing all the points of multiplicity at least 3. We show that if \A is a line arrangement in the classes \CC_k for k≤ 2, then any rank one local system \LL on the line arrangement complement M is admissible. Partial results are obtained for the class \CC₃.

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