2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125419This 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 friendshipAlgebraic GeometryAlgebraic Topology14F35, 32S60text