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On Deformations of Pairs (Manifold, Coherent Sheaf)

Part of: Commutative algebra: Homological methods Homological algebra Families, fibrations Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  09 January 2019

Donatella Iacono  and
Marco Manetti
Donatella Iacono
Affiliation:
Università degli Studi di Bari, Dipartimento di Matematica, Via E. Orabona 4, I-70125 Bari, Italy Email: donatella.iacono@uniba.it
Marco Manetti
Affiliation:
Università degli Studi di Roma “La Sapienza”, Dipartimento di Matematica “Guido Castelnuovo”, P.le Aldo Moro 5, I-00185 Roma, Italy Email: manetti@mat.uniroma1.it
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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.

Keywords

deformation of manifold and coherent sheafdifferential graded Lie algebra

MSC classification

Primary: 14D15: Formal methods; deformations
Secondary: 13D10: Deformations and infinitesimal methods 17B70: Graded Lie (super)algebras 18G50: Nonabelian homological algebra
Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 5 , October 2019 , pp. 1209 - 1241
Copyright
© Canadian Mathematical Society 2018 

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Footnotes

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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