Lagrangian Fibrations onto Varieties with Isolated Quotient Singularities
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912778328997888 |
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| author | Müller, Niklas Xu, Zheng |
| author_facet | Müller, Niklas Xu, Zheng |
| contents | In this note, we show that if $f\colon M\rightarrow X$ is a germ of a projective Lagrangian fibration from a holomorphic symplectic manifold $M$ onto a normal analytic variety $X$ with isolated quotient singularities, then $X$ is smooth. In particular, if $f\colon M\rightarrow X$ is a Lagrangian fibration from a hyper-Kähler fourfold $M$ onto a normal surface $X$, then $X\cong \mathbb{P}^2$, which recovers a recent result of Huybrechts--Xu and Ou. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04135 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lagrangian Fibrations onto Varieties with Isolated Quotient Singularities Müller, Niklas Xu, Zheng Algebraic Geometry 14J42, 14B05, 14D06 In this note, we show that if $f\colon M\rightarrow X$ is a germ of a projective Lagrangian fibration from a holomorphic symplectic manifold $M$ onto a normal analytic variety $X$ with isolated quotient singularities, then $X$ is smooth. In particular, if $f\colon M\rightarrow X$ is a Lagrangian fibration from a hyper-Kähler fourfold $M$ onto a normal surface $X$, then $X\cong \mathbb{P}^2$, which recovers a recent result of Huybrechts--Xu and Ou. |
| title | Lagrangian Fibrations onto Varieties with Isolated Quotient Singularities |
| topic | Algebraic Geometry 14J42, 14B05, 14D06 |
| url | https://arxiv.org/abs/2508.04135 |