On the discriminant locus of a Lagrangian fibration

Details On the discriminant locus of a Lagrangian fibration On the discriminant locus of a Lagrangian fibration

2006-07-21

arxiv.org/abs/math/0607558v1

Math. Ann. 341 (2008), no. 1, 201-221

Mathematics

Algebraic Geometry

17 pages

Scientific paper

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

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