Characteristic varieties and constructible sheaves

  • Alexandru Dimca

    Université de Nice Sophia Antipolis, France


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 paper [1], 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 [3]. The new point of view is the key role played by the constructible sheaves naturally arising from local systems.

Cite this article

Alexandru Dimca, Characteristic varieties and constructible sheaves. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 4, pp. 365–389

DOI 10.4171/RLM/503