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On a generalized Batyrev’s cone conjecture

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Abstract

We discuss some variants of cone theorem for movable curves in any codimension.

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Acknowledgements

The first author was partially supported by NRF-2016R1C1B2011446. Some parts of this paper were written during the first author’s visits to University of Tokyo, Osaka University and IBS-Center for Geometry and Physics. He is grateful for their hospitality. The second author was partially supported by JSPS KAKENHI \(\#\)15H03611, 16H02141, 17H02831, and 18H01108. He thanks Professors Tommaso de Fernex, Masayuki Kawakita, János Kollár, and Keiji Oguiso for comments, questions, and discussion. He brushed up this paper when he stayed at MSRI, Johns Hopkins University, National Taiwan University, and University of Utah. He is grateful to it for their hospitality. Lastly, both authors are grateful for the referee’s numerous suggestions to the previous versions of the paper.

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Authors and Affiliations

  1. Department of mathematics, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul, 03722, South Korea

    Sung Rak Choi

  2. Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Yoshinori Gongyo

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  1. Sung Rak Choi
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  2. Yoshinori Gongyo
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Correspondence to Sung Rak Choi.

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Choi, S.R., Gongyo, Y. On a generalized Batyrev’s cone conjecture. Math. Z. 300, 1319–1334 (2022). https://doi.org/10.1007/s00209-021-02813-8

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  • DOI: https://doi.org/10.1007/s00209-021-02813-8

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