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2 results

  • On Deformations of Pairs (Manifold, Coherent Sheaf)

  • Part of
  • Donatella Iacono, Marco Manetti
  • Journal:
    Canadian Journal of Mathematics / Volume 71 / Issue 5 / October 2019
    Published online by Cambridge University Press:
    09 January 2019, pp. 1209-1241
    Print publication:
    October 2019
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  • We analyse infinitesimal deformations of pairs $(X,{\mathcal{F}})$ with ${\mathcal{F}}$ a coherent sheaf on a smooth projective variety $X$ over an algebraically closed field of characteristic 0. We describe a differential graded Lie algebra controlling the deformation problem, and we prove an analog of a Mukai–Artamkin theorem about the trace map.

  • Cohomology jump loci of differential graded Lie algebras

  • Part of
  • Nero Budur, Botong Wang
  • Journal:
    Compositio Mathematica / Volume 151 / Issue 8 / August 2015
    Published online by Cambridge University Press:
    06 March 2015, pp. 1499-1528
    Print publication:
    August 2015
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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.