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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.00395 |
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| _version_ | 1866913373625516032 |
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| author | Abuaf, Roland Carini, Riccardo |
| author_facet | Abuaf, Roland Carini, Riccardo |
| contents | Let $\mathcal{M}_{C}(2, 0)$ be the moduli space of semistable rank two and degree zero Higgs bundles on a smooth complex hyperelliptic curve $C$ of genus three. We prove that the quotient of $\mathcal{M}_{C}(2, 0)$ by a twisted version of the hyperelliptic involution is an 18-dimensional holomorphic symplectic variety admitting a crepant resolution, whose local model was studied by Kaledin and Lehn to describe O'Grady's singularities. Similarly, by considering the moduli space of Higgs bundles with trivial determinant $\mathcal{M}_C(2, \mathcal{O}_{C})\subseteq \mathcal{M}_C(2, 0)$, we show that the quotient of $\mathcal{M}_C(2, \mathcal{O}_{C})$ by the hyperelliptic involution is a 12-dimensional holomorphic symplectic variety admitting a crepant resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holomorphic symplectic manifolds from semistable Higgs bundles Abuaf, Roland Carini, Riccardo Algebraic Geometry 14J42, 14D20 Let $\mathcal{M}_{C}(2, 0)$ be the moduli space of semistable rank two and degree zero Higgs bundles on a smooth complex hyperelliptic curve $C$ of genus three. We prove that the quotient of $\mathcal{M}_{C}(2, 0)$ by a twisted version of the hyperelliptic involution is an 18-dimensional holomorphic symplectic variety admitting a crepant resolution, whose local model was studied by Kaledin and Lehn to describe O'Grady's singularities. Similarly, by considering the moduli space of Higgs bundles with trivial determinant $\mathcal{M}_C(2, \mathcal{O}_{C})\subseteq \mathcal{M}_C(2, 0)$, we show that the quotient of $\mathcal{M}_C(2, \mathcal{O}_{C})$ by the hyperelliptic involution is a 12-dimensional holomorphic symplectic variety admitting a crepant resolution. |
| title | Holomorphic symplectic manifolds from semistable Higgs bundles |
| topic | Algebraic Geometry 14J42, 14D20 |
| url | https://arxiv.org/abs/2406.00395 |