Characteristic varieties and constructible sheaves

Details Characteristic varieties and constructible sheaves Characteristic varieties and constructible sheaves

2007-02-28

arxiv.org/abs/math/0702871v2

Rend. Lincei Mat. Appl. 18(2007), 365- 389.

Mathematics

Algebraic Geometry

This new version brings in the orbifold fundamental groups and gives a simple, complete description of the finite group $T(f)$

Scientific paper

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.

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