Anti-symplectic involutions on moduli spaces of sheaves on K3 surfaces via auto-equivalences
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912494090452992 |
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| author | Faenzi, Daniele Menet, Grégoire Prieto-Montañez, Yulieth |
| author_facet | Faenzi, Daniele Menet, Grégoire Prieto-Montañez, Yulieth |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anti-symplectic involutions on moduli spaces of sheaves on K3 surfaces via auto-equivalences Faenzi, Daniele Menet, Grégoire Prieto-Montañez, Yulieth Algebraic Geometry 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. |
| title | Anti-symplectic involutions on moduli spaces of sheaves on K3 surfaces via auto-equivalences |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.12668 |