Alexandru Dimca
Published 2007-02-28, updated 2007-05-18Version 2
We explore the relation between the positive dimensional irreducible components of the characteristic varieties of rank one local systems on a smooth surface and the associated (rational or irrational) pencils. Our study, which may viewed as a continuation of D. Arapura's work, yields new geometric insight into the translated components relating them to the multiplicities of curves in the associated pencil, in a close analogy to the compact situation treated by A. Beauville. The new point of view is the key role played by the constructible sheaves naturally arising from local systems.
Comments: This new version brings in the orbifold fundamental groups and gives a simple, complete description of the finite group $T(f)$, see Theorem 5.3, which corrects a previous result by Serrano
Journal: Rend. Lincei Mat. Appl. 18(2007), 365- 389.
Pencils of plane curves and characteristic varieties
Triples of arrangements and local systems
Rank one local systems and forms of degree one
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