We study relations between the quadraticity of the Kuranishi family of a coherent sheaf on a complex projective scheme and the formality of the DG-Lie algebra of its derived endomorphisms. In particular, we prove that for a polystable coherent sheaf of a smooth complex projective surface the DG-Lie algebra of derived endomorphisms is formal if and only if the Kuranishi family is quadratic.

Deformations of polystable sheaves on surfaces: quadraticity implies formality

Meazzini F.
2022

Abstract

We study relations between the quadraticity of the Kuranishi family of a coherent sheaf on a complex projective scheme and the formality of the DG-Lie algebra of its derived endomorphisms. In particular, we prove that for a polystable coherent sheaf of a smooth complex projective surface the DG-Lie algebra of derived endomorphisms is formal if and only if the Kuranishi family is quadratic.
2022
Bandiera R.; Manetti M.; Meazzini F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/896933
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