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 / Bandiera R.; Manetti M.; Meazzini F.. - In: MOSCOW MATHEMATICAL JOURNAL. - ISSN 1609-3321. - STAMPA. - 22:2(2022), pp. 239-263. [10.17323/1609-4514-2022-22-2-239-263]
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.| File | Dimensione | Formato | |
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