Intersection of two quadrics: modular interpretation and Hitchin morphism
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912415001608192 |
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| author | Benedetti, Vladimiro Höring, Andreas Liu, Jie |
| author_facet | Benedetti, Vladimiro Höring, Andreas Liu, Jie |
| contents | The cotangent bundle $T^*X$ of a smooth intersection $X$ of two quadrics admits a Lagrangian fibration determined by the intrinsic geometry of $X$. We show that this fibration is actually the Hitchin morphism if we endow $X$ with a structure of moduli space of twisted Spin-bundles. This generalises the classical result for threefolds, in which case it recovers the Hitchin fibration for the moduli space of rank two bundles with fixed determinant of odd degree on a curve of genus two. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_04707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersection of two quadrics: modular interpretation and Hitchin morphism Benedetti, Vladimiro Höring, Andreas Liu, Jie Algebraic Geometry 14H60, 14D20, 14J45, 14M10 The cotangent bundle $T^*X$ of a smooth intersection $X$ of two quadrics admits a Lagrangian fibration determined by the intrinsic geometry of $X$. We show that this fibration is actually the Hitchin morphism if we endow $X$ with a structure of moduli space of twisted Spin-bundles. This generalises the classical result for threefolds, in which case it recovers the Hitchin fibration for the moduli space of rank two bundles with fixed determinant of odd degree on a curve of genus two. |
| title | Intersection of two quadrics: modular interpretation and Hitchin morphism |
| topic | Algebraic Geometry 14H60, 14D20, 14J45, 14M10 |
| url | https://arxiv.org/abs/2506.04707 |