On the irreducible components of characteristic varieties

Abstract

This is a quick survey on the characteristic varieties associated to rank one local systems on a smooth, irreducible, quasi-projective complex variety $M$. A key new result is Proposition 1.8, giving additional information on the constructible sheaf $\F=R^0f_*(\LL)$, where $\LL$ is a rank one local system on $M$ and $f:M\to S$ is a surjective morphism with $S$ a smooth curve and the generic fiber $F$ of $f$ connected. Corollary 1.9 says that for $S$ compact, the singular support of $\F$ cannot be a singleton.

This is a paper dedicated to the 60th anniversary of Dorin Popescu, as a sign of a life-long friendship

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• Non-finiteness properties of fundamental groups of smooth projective varieties
• Formality, Alexander invariants, and a question of Serre
• Unitary local systems, multiplier ideals, and polynomial periodicity of Hodge numbers
• Quasi-Kähler Bestvina-Brady groups
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Cited by in corpus (6)

• Resonance varieties and Dwyer-Fried invariants
• Recent results on cohomology jump loci
• Characteristic varieties of graph manifolds and quasi-projectivity of fundamental groups of algebraic links
• Generalized Broughton polynomials and characteristic varieties
• $L^2$-type invariants and cohomology jump loci for complex smooth quasi-projective varieties
• On admissible rank one local systems