Cohomology jump loci of differential graded Lie algebras

Publisher: Cambridge University Press

E-ISSN: 1570-5846|151|8|1499-1528

ISSN: 0010-437x

Source: Compositio Mathematica, Vol.151, Iss.8, 2015-08, pp. : 1499-1528

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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.