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Kodaira dimension of algebraic fiber spaces over abelian varieties

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Abstract

In this article we provide a proof of the Iitaka \(C_{nm}\) conjecture for algebraic fiber spaces over tori.

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Notes

  1. We can add this assumption by the argument in the beginning of Theorem 4.4.

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Acknowledgments

We owe a debt of gratitude to Bo Berndtsson, Sébastien Boucksom, Frédéric Campana, Philippe Eyssidieux, Christopher Hacon, Andreas Höring, Zhi Jiang, Yujiro Kawamata, Mihnea Popa, Hossein Raufi, Christian Schnell and Shigeharu Takayama for sharing generously with us their results and intuitions on the topics analyzed here. It is our pleasure to acknowledge the partial support we have benefited from the ANR project “MACK” during the preparation of the present article. Last but not least, we would like to thank the anonymous referee for constructive criticism and excellent suggestions who helped us to improve substantially the quality of this work.

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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu, Université Paris 6, 4, Place Jussieu, 75252, Paris, France

    Junyan Cao

  2. Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, 130-722, South Korea

    Mihai Păun

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  1. Junyan Cao
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  2. Mihai Păun
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Correspondence to Junyan Cao.

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Cao, J., Păun, M. Kodaira dimension of algebraic fiber spaces over abelian varieties. Invent. math. 207, 345–387 (2017). https://doi.org/10.1007/s00222-016-0672-6

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