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

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arxiv 2409.12668 v2 pith:LFKFO43R submitted 2024-09-19 math.AG

Daniele Faenzi (IMB) , Grégoire Menet (IMB) , Yulieth Prieto-Montañez (UC) This is my paper
classification math.AG
keywords involutionsmodulisheavessurfacesanti-symplecticconstructionexamplesspaces
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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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  1. More birational involutions

    math.AG 2025-09 conditional novelty 6.0 of 10

    A birational involution on Hilbert schemes of points on K3 surfaces, earlier found by lattice-theoretic counting, is described geometrically and its indeterminacy locus is identified as a P2-fibration over a moduli sp...

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