On symplectic birational self-maps of projective hyperkähler manifolds of K3$^{[n]}$-type
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866911910205587456 |
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| author | Dutta, Yajnaseni Mattei, Dominique Prieto-Montañez, Yulieth |
| author_facet | Dutta, Yajnaseni Mattei, Dominique Prieto-Montañez, Yulieth |
| contents | We prove that projective hyperkähler manifolds of K3$^{[n]}$-type admitting a non-trivial symplectic birational self-map of finite order are isomorphic to moduli spaces of stable (twisted) coherent sheaves on K3 surfaces. Motivated by this result, we analyze the reflections on the movable cone of moduli spaces of sheaves and determine when they come from a birational involution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03783 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On symplectic birational self-maps of projective hyperkähler manifolds of K3$^{[n]}$-type Dutta, Yajnaseni Mattei, Dominique Prieto-Montañez, Yulieth Algebraic Geometry 14J50, 14E05, 14D20, 14C05 We prove that projective hyperkähler manifolds of K3$^{[n]}$-type admitting a non-trivial symplectic birational self-map of finite order are isomorphic to moduli spaces of stable (twisted) coherent sheaves on K3 surfaces. Motivated by this result, we analyze the reflections on the movable cone of moduli spaces of sheaves and determine when they come from a birational involution. |
| title | On symplectic birational self-maps of projective hyperkähler manifolds of K3$^{[n]}$-type |
| topic | Algebraic Geometry 14J50, 14E05, 14D20, 14C05 |
| url | https://arxiv.org/abs/2209.03783 |