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manuscripta mathematica

, Volume 151, Issue 3–4, pp 305–327 | Cite as

On polarization types of Lagrangian fibrations

  • Benjamin WieneckEmail author
Article

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 \(\text {K}3^{[n]}\)-type fibrations and conjecture that the polarization type should only depend on the deformation type of the total space.

Mathematics Subject Classification

32J27 14D06 32Q15 53D12 53C26 32G13 14D20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institut für Algebraische GeometrieLeibniz Universität HannoverHannoverGermany

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