Derived automorphism groups of K3 surfaces of Picard rank 1

Abstract

We give a complete description of the group of exact autoequivalences of the bounded derived category of coherent sheaves on a K3 surface of Picard rank 1. We do this by proving that a distinguished connected component of the space of stability conditions is preserved by all autoequivalences, and is contractible.

37 pages. v2: expository improvements. v3: further expository improvements based on referee comments. To appear in Duke Math. J

References in corpus (2)

• MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations
• Stability conditions and quantum dilogarithm identities for Dynkin quivers

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