Deformations of polystable sheaves on surfaces: quadraticity implies formality
Algebraic Geometry
2020-06-18 v3 Representation Theory
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 on a smooth complex projective surface the DG-Lie algebra of derived endomorphisms is formal if and only if the Kuranishi family is quadratic.
Keywords
Cite
@article{arxiv.1902.06486,
title = {Deformations of polystable sheaves on surfaces: quadraticity implies formality},
author = {Ruggero Bandiera and Marco Manetti and Francesco Meazzini},
journal= {arXiv preprint arXiv:1902.06486},
year = {2020}
}
Comments
V3 post-print version; accepted for publication in Moscow Mathematical Journal