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Cohomology jump loci of differential graded Lie algebras

Part of: Deformations of analytic structures (Co)homology theory Families, fibrations

Published online by Cambridge University Press:  06 March 2015

Nero Budur  and
Botong Wang
Nero Budur
Affiliation:
KU Leuven, Belgium University of Notre Dame, USA email Nero.Budur@wis.kuleuven.be Current address: KU Leuven, Department of Mathematics, Celestijnenlaan 200B, B-3001 Leuven, Belgium
Botong Wang
Affiliation:
Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, IN 46556, USA email bwang3@nd.edu
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Abstract

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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.

Keywords

deformation theorydifferential graded Lie algebracohomology jump locuslocal system

MSC classification

Primary: 14D15: Formal methods; deformations 32G08: Deformations of fiber bundles 14F35: Homotopy theory; fundamental groups
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 8 , August 2015 , pp. 1499 - 1528
Copyright
© The Authors 2015 

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