On polarization types of Lagrangian fibrations

Abstract

The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization type is constant in families of Lagrangian fibrations. Further, we determine the polarization type of K3^[n]-type fibrations and conjecture that the polarization type should only depend on the deformation type of the total space.

25 pages. Corrected and improved version, thanks to the referee. The paper will appear in Manuscripta Mathematica

References in corpus (3)

• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• Base manifolds for fibrations of projective irreducible symplectic manifolds
• Base manifolds for Lagrangian fibrations on hyperkähler manifolds

Cited by in corpus (1)

• Monodromy Invariants and Polarization Types of Generalized Kummer Fibrations