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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.