O'Grady tenfolds as moduli spaces of sheaves
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929319081672704 |
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| author | Felisetti, Camilla Giovenzana, Franco Grossi, Annalisa |
| author_facet | Felisetti, Camilla Giovenzana, Franco Grossi, Annalisa |
| contents | We give a lattice-theoretic characterization for a manifold of $\mathrm{OG}10$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li-Pertusi-Zhao variety of $\mathrm{OG}10$ type associated to any smooth cubic fourfold. Moreover we determine when a birational transformation is induced by an automorphism of the K3 surface and we use this to classify all induced birational symplectic involutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_07017 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | O'Grady tenfolds as moduli spaces of sheaves Felisetti, Camilla Giovenzana, Franco Grossi, Annalisa Algebraic Geometry 14J42, 14E07 (14J50) We give a lattice-theoretic characterization for a manifold of $\mathrm{OG}10$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li-Pertusi-Zhao variety of $\mathrm{OG}10$ type associated to any smooth cubic fourfold. Moreover we determine when a birational transformation is induced by an automorphism of the K3 surface and we use this to classify all induced birational symplectic involutions. |
| title | O'Grady tenfolds as moduli spaces of sheaves |
| topic | Algebraic Geometry 14J42, 14E07 (14J50) |
| url | https://arxiv.org/abs/2303.07017 |