Cohomology jump loci of differential graded Lie algebras

Abstract

To study infinitesimal deformation problems with cohomology constraints, we introduce and study cohomology jump functors for differential graded Lie algebra (DGLA) pairs. We apply this to local systems, vector bundles, Higgs bundles, and representations of fundamental groups. The results obtained describe the analytic germs of the cohomology jump loci inside the corresponding moduli space, extending previous results of Goldman-Millson, Green-Lazarsfeld, Nadel, Simpson, Dimca-Papadima, and of the second author.

final version to appear in Compositio Math

References in corpus (5)

• Topology and geometry of cohomology jump loci
• Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves
• Examples of topological spaces with arbitrary cohomology jump loci
• Cohomology jump loci of compact Kähler manifolds
• Cohomology jump loci in the moduli spaces of vector bundles

Cited by in corpus (11)

• Around the tangent cone theorem
• Abelian duality and propagation of resonance
• Recent results on cohomology jump loci
• Perverse sheaves on semi-abelian varieties
• Naturality properties and comparison results for topological and infinitesimal embedded jump loci
• Infinitesimal finiteness obstructions
• Cohomology jump loci of 3-manifolds
• Rank two topological and infinitesimal embedded jump loci of quasi-projective manifolds
• Mixed Hodge structures on cohomology jump ideals
• Generic Vanishing, 1-forms, and Topology of Albanese Maps
• Deformations of morphisms of sheaves