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Alpha invariants of birationally bi-rigid Fano 3-folds I

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Abstract

We compute global log canonical thresholds of certain birationally bi-rigid Fano 3-folds embedded in weighted projective spaces as complete intersections of codimension 2 and prove that they admit an orbifold Kähler–Einstein metric and are K-stable. As an application, we give examples of super-rigid affine Fano 4-folds.

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Acknowledgements

The authors would like to thank the referees for useful suggestions which improved the introduction.

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Authors and Affiliations

  1. Department of mathematics, Yonsei University, Seoul, 03722, Republic of Korea

    In-Kyun Kim

  2. Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502, Japan

    Takuzo Okada

  3. Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul, 02455, Republic of Korea

    Joonyeong Won

Authors
  1. In-Kyun Kim
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  2. Takuzo Okada
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  3. Joonyeong Won
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Correspondence to Joonyeong Won.

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The first author was supported by the National Research Foundation of Korea (NRF-2020R1A2C4002510). The second author is partially supported by JSPS KAKENHI Grant Number JP18K03216. The third author was supported by the National Research Foundation of Korea (NRF-2020R1A2C1A01008018) and a KIAS Individual Grant (SP037003) via the Center for Mathematical Challenges at Korea Institute for Advanced Study.

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Kim, IK., Okada, T. & Won, J. Alpha invariants of birationally bi-rigid Fano 3-folds I. European Journal of Mathematics 7, 272–308 (2021). https://doi.org/10.1007/s40879-020-00441-w

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  • DOI: https://doi.org/10.1007/s40879-020-00441-w

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