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On Deformations of Pairs (Manifold, Coherent Sheaf)

  • Donatella Iacono (a1) and Marco Manetti (a2)
Abstract

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.

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Author D. I. acknowledges the support of Fondi di Ateneo dell’Università di Bari. Author M. M. acknowledges the support by Italian MIUR under PRIN project 2015ZWST2C “Moduli spaces and Lie theory”.

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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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