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arXiv · 2508.04135

Lagrangian Fibrations onto Varieties with Isolated Quotient Singularities

Niklas Müller·Zheng Xu
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Abstract

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.

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Niklas Müller, Zheng Xu. 2025-12-21. Lagrangian Fibrations onto Varieties with Isolated Quotient Singularities. https://arxiv.org/abs/2508.04135

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