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On almost holomorphic Lagrangian fibrations

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Abstract

We prove that the pull back of an ample line bundle by an almost holomorphic Lagrangian fibration is nef. As an application, we show birational semi rigidity of Lagrangian fibrations.

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Acknowledgments

The author would like to express his thanks to Professors Christian Lehn and Ekaterina Amerik for their comments. He also would like to express his thanks to Professor Keiji Oguiso who taught him Example 1.

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Authors and Affiliations

  1. Division of Mathematics, Graduate School of Science, Hokkaido University, Sapporo, 060-0810, Japan

    Daisuke Matsushita

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  1. Daisuke Matsushita
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Correspondence to Daisuke Matsushita.

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Partially supported by Grand-in-Aid # 18684001 (Japan Society for Promotion of Sciences)

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Matsushita, D. On almost holomorphic Lagrangian fibrations. Math. Ann. 358, 565–572 (2014). https://doi.org/10.1007/s00208-013-0964-8

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  • DOI: https://doi.org/10.1007/s00208-013-0964-8

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