Central derived autoequivalences of K3 surfaces

TL;DR

This paper uses Bridgeland stability conditions to characterize the central autoequivalences of the derived category of a complex K3 surface, providing insights into its symmetry structure.

Contribution

It introduces a novel application of Bridgeland stability conditions to explicitly describe the center of the autoequivalence group of K3 surfaces.

Findings

Identifies the central autoequivalences using stability conditions.

Provides a new perspective on the symmetry group of K3 surfaces.

Enhances understanding of derived autoequivalence groups.

Abstract

We apply the theory of Bridgeland's stability conditions to describe the center of the group $\mathrm{Aut}(\mathrm{D}^b(X))$ of bounded derived autoequivalences of a complex projective K3 surface.