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On the discriminant locus of a Lagrangian fibration

Justin Sawon
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Abstract

Let $X\to¶^n$ be an irreducible holomorphic symplectic manifold of dimension $2n$ fibred over $¶^n$. Matsushita proved that the generic fibre is a holomorphic Lagrangian abelian variety. In this article we study the discriminant locus $Δ\subset¶^n$ parametrizing singular fibres. Our main result is a formula for the degree of $Δ$, leading to bounds on the degree when $X$ is a four-fold.

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Justin Sawon. 2006-07-21. On the discriminant locus of a Lagrangian fibration. https://arxiv.org/abs/math/0607558

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