On the irreducible components of characteristic varieties

2007/03/09 by Alexandru Dimca, Dimca, Alexandru
Mathematics · #14F35 #32S60 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT #msc:14F35 #msc:32S60

paper · pdf · doi:10.48550/arxiv.math/0703257

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

arxiv created 2007/03/09 · arxiv updated 2009/12/01

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=R⁰f_*(\LL), where \LL is a rank one local system on M and f:M → 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.

Related

• Rank one local systems and forms of degree one
• On the reducibility of characteristic varieties
• Local systems which do not come from abelian varieties
• Rigid non-cohomologically rigid local systems
• The Singular Supports of IC sheaves on Quasimaps' Spaces are Irreducible