Cohomology jump loci of compact Kähler manifolds

2013/03/27 by Botong Wang, Wang, Botong
Mathematics · #14B12 #14F35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1303.6937

openalex publication_date 2013/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply the method of Dimca-Papadima to study the cohomology jump loci in the representation variety and the moduli space of vector bundles with vanishing chern classes for a compact Kähler manifold. We introduce modules over differential graded Lie algebra to extend results of Dimca-Papadima to a general point in the representation variety or the moduli space. We show that locally the cohomology jump loci is isomorphic to the resonance variety via the exponential map. This paper generalizes a previous result of the author.

Citations

• Cohomology jump loci of quasi-projective varieties

Related

• Cohomology jump loci in the moduli spaces of vector bundles
• Cohomology jump loci of quasi-compact Kähler manifolds
• Torsion points on the cohomology jump loci of compact Kähler manifolds
• Recent results on cohomology jump loci
• Cohomology jump loci of quasi-projective varieties