  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.
