Torsor Neron models of hyperkahler manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916950751313920 |
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| author | Kamenova, Ljudmila Verbitsky, Misha |
| author_facet | Kamenova, Ljudmila Verbitsky, Misha |
| contents | Let $M$ be a compact hyperkahler manifold equipped with a Lagrangian fibration $π:\; M \to X$, and $M'$ the smooth locus of $π$. We prove that over a complement to a codimension $\geq 2$ subset in $X$, the projection $π:\; M' \to X$ has a natural structure of a torsor over an abelian group bundle, which can be understood as a complex analytic variant of the Néron model construction. This gives an independent proof of a result by Y.-J. Kim. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torsor Neron models of hyperkahler manifolds Kamenova, Ljudmila Verbitsky, Misha Algebraic Geometry Let $M$ be a compact hyperkahler manifold equipped with a Lagrangian fibration $π:\; M \to X$, and $M'$ the smooth locus of $π$. We prove that over a complement to a codimension $\geq 2$ subset in $X$, the projection $π:\; M' \to X$ has a natural structure of a torsor over an abelian group bundle, which can be understood as a complex analytic variant of the Néron model construction. This gives an independent proof of a result by Y.-J. Kim. |
| title | Torsor Neron models of hyperkahler manifolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.12369 |