Let F be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the differential graded (DG) Lie algebra RHom(F, F) of derived endomorphisms of F is formal. The proof is based on the study of equivariant L-infinity minimal models of DG Lie algebras equipped with a cyclic structure of degree 2 which is non-degenerate in cohomology, and does not rely (even for K3 surfaces) on previous results on the same subject.
Bandiera, R., Manetti, M., Meazzini, F. (2021). Formality conjecture for minimal surfaces of Kodaira dimension 0. COMPOSITIO MATHEMATICA, 157(2), 215-235 [10.1112/S0010437X20007605].
Formality conjecture for minimal surfaces of Kodaira dimension 0
Meazzini, F.
2021
Abstract
Let F be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the differential graded (DG) Lie algebra RHom(F, F) of derived endomorphisms of F is formal. The proof is based on the study of equivariant L-infinity minimal models of DG Lie algebras equipped with a cyclic structure of degree 2 which is non-degenerate in cohomology, and does not rely (even for K3 surfaces) on previous results on the same subject.File in questo prodotto:
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