On the discriminant locus of a Lagrangian fibration

Abstract:

Let X->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 in 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.

Appears in Volume 341 (2008) No. 1 of Mathematische Annalen. Available as math.AG/0607558 from the e-Print archive.

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