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