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arXiv · 1501.04489

On polarization types of Lagrangian fibrations

Benjamin Wieneck
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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.

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Benjamin Wieneck. 2016-04-26. On polarization types of Lagrangian fibrations. https://doi.org/10.1007/s00229-016-0845-z

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