Formality conjecture for K3 surfaces

Abstract

We give a proof of the formality conjecture of Kaledin and Lehn: on a complex projective K3 surface, the DG algebra RHom(F,F) is formal for any sheaf F polystable with respect to an ample line bundle. Our main tool is the uniqueness of DG enhancement of the bounded derived category of coherent sheaves. We also extend the formality result to derived objects that are polystable with respect to a generic Bridgeland stability condition.

final version, to appear in Compos. Math

References in corpus (2)

• Moduli stacks of semistable sheaves and representations of Ext-quivers
• Formality conjecture for K3 surfaces

Cited by in corpus (3)

• Formality conjecture for K3 surfaces
• Formality conjecture for minimal surfaces of Kodaira dimension 0
• Rational singularities for moment maps of totally negative quivers