Singular fibres of very general Lagrangian fibrations

Abstract

Let $\pi :X\to {\mathbb{P}}^n$ be a (holomorphic) Lagrangian fibration that is very general in the moduli space of Lagrangian fibrations. We conjecture that the singular fibres in codimension one must be semistable degenerations of abelian varieties. We prove a partial result towards this conjecture, and describe an example that provides further evidence.

19 pages, 3 figures

References in corpus (3)

• Base manifolds for fibrations of projective irreducible symplectic manifolds
• Monodromy Invariants and Polarization Types of Generalized Kummer Fibrations
• A finiteness theorem for Lagrangian fibrations

Cited by in corpus (1)

• The Intermediate Jacobian fibration of a cubic fourfold containing a plane and fibrations in Prym varieties