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arXiv · 1905.03386

Singular fibres of very general Lagrangian fibrations

Justin Sawon
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Abstract

Let $\pi:X\rightarrow\mathbb{P}^n$ be a (holomorphic) Lagrangian fibration that is very general in the moduli space of Lagrangian fibrations. We conjecture that the singular fibres in codimension one must be semistable degenerations of abelian varieties. We prove a partial result towards this conjecture, and describe an example that provides further evidence.

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Justin Sawon. 2019-05-08. Singular fibres of very general Lagrangian fibrations. https://doi.org/10.1142/s021919972150070x

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