Anti-symplectic involutions on moduli spaces of sheaves on K3 surfaces via auto-equivalences

TL;DR

This paper introduces new anti-symplectic involutions on moduli spaces of sheaves on K3 surfaces, constructed via derived autoequivalences from spherical bundles, extending classical examples and unifying various constructions.

Contribution

It provides novel examples of anti-symplectic involutions on K3 moduli spaces using autoequivalences from spherical bundles, expanding the understanding of symplectic geometry in this context.

Findings

Constructed new anti-symplectic involutions via derived autoequivalences.

Extended classical involutions like Beauville and Markman-O'Grady.

Unified different known involution constructions on K3 moduli spaces.

Abstract

We provide new examples of anti-symplectic involutions on moduli spaces of stable sheaves on K3 surfaces. These involutions are constructed through (anti) autoequivalences of the bounded derived category of coherent sheaves on K3 surfaces arising from spherical bundles. We analyze these induced maps in the moduli space, imposing restrictions on the Mukai vector and considering the preservation of stability conditions. Our construction extends and unifies classical examples, such as the Beauville involutions, Markman-O'Grady reflections and a more recent construction by Beri-Manivel.