Formality conjecture for minimal surfaces of Kodaira dimension 0

Abstract

Let F be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the DG-Lie algebra RHom(F,F) of derived endomorphisms of F is formal. The proof is based on the study of equivariant $L_{\infty }$ 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.

arXiv commentPost-print version; accepted for publication in Compositio Mathematica

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Cited by in corpus (1)

• Connections and $L_{\infty }$ liftings of semiregularity maps