Cohomology jump loci of quasi-projective varieties

2012/11/15 by Nero Budur, Botong Wang, Budur, Nero +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.1211.3766

Final version, to appear in Ann. Sci. Ecole Norm. Sup

openalex publication_date 2012/11/15 · arxiv created 2014/04/08 · arxiv updated 2014/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the cohomology jump loci in the space of rank one local systems over a smooth quasi-projective variety are finite unions of torsion translates of subtori. The main ingredients are a recent result of Dimca-Papadima, some techniques introduced by Simpson, together with properties of the moduli space of logarithmic connections constructed by Nitsure and Simpson.

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• Cohomology jump loci of compact Kähler manifolds

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