Monodromy of local systems on the complement of line arrangements

Abstract

We show that a previous construction for fibered arrangements can be generalized to obtain new algebraic complexes computing the local system (co)homology of any (affine) line arrangement. We obtain a description of the characteristic variety as the locus where the monodromies around the singular points of the arrangement share a common fixed subspace. We apply this construction to the problem of deciding whether the monodromy action on the homology of the Milnor fiber is trivial. In particular, we improve a previous result motivated by the a-monodromicity conjecture stated by the second author.