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Deformations of polystable sheaves on surfaces: quadraticity implies formality

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arxiv 1902.06486 v3 pith:OJZ2SJBW submitted 2019-02-18 math.AG math.RT

Ruggero Bandiera , Marco Manetti , Francesco Meazzini This is my paper · ORCID
classification math.AGmath.RT
keywords algebracoherentcomplexderiveddg-lieendomorphismsfamilyformality
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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 on a smooth complex projective surface the DG-Lie algebra of derived endomorphisms is formal if and only if the Kuranishi family is quadratic.

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  1. Some examples of DG-Lie formality transfer

    math.RA 2026-01 accept novelty 6.0 of 10

    A DG-Lie formality-transfer theorem is extended with a new backward direction and applied to universal enveloping algebras and finite quotients of Kodaira-Spencer algebras.

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