A. Dimca
Published 2006-06-19, updated 2006-07-13Version 3
We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M. Falk and S. Yuzvinsky in the case of line arrangements, see mathAG/0603166. In this case, this geometric point of view was already hinted to by A. Libgober and S. Yuzvinsky. Our study yields new geometric insight on the translated components of the characteristic varieties, relating them to the multiplicities of curves in the associated pencil, in close analogy to the compact situation treated by A. Beauville.
Comments: New results: First Prop. 3.18, Cor. 3.21 and Prop. 6.7 saying that all the possible translates actually do occur as components. Next Cor. 6.8 and Example 6.11 showing that the various translates are irreducible components of various characteristic varieties $\V_m(M)$. We have added a key reference to Beauville's related work and have discarded the claims about combinatorial determinacy, since they were not fully proved
Characteristic varieties and constructible sheaves
Characteristic varieties of quasi-projective manifolds and orbifolds
Generalized Broughton polynomials and characteristic varieties
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