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arXiv · 2409.12668

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

Daniele Faenzi·Grégoire Menet·Yulieth Prieto-Montañez
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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.

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Daniele Faenzi, Grégoire Menet, Yulieth Prieto-Montañez. 2024-09-19. Anti-symplectic involutions on moduli spaces of sheaves on K3 surfaces via auto-equivalences. https://arxiv.org/abs/2409.12668

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