On the irreducible components of characteristic varieties

Details On the irreducible components of characteristic varieties On the irreducible components of characteristic varieties

2007-03-09

arxiv.org/abs/math/0703257v1

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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