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Surfaces of globally F-regular and F-split type

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Abstract

We prove that normal projective surfaces of dense globally F-split type (respectively, globally F-regular type) are of Calabi–Yau type (respectively, Fano type).

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Notes

  1. The notions of global F-splitting and global F-regularity can be extended to a pair of a normal projective variety and a divisor on it. See Definition 2.5 for the details.

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Acknowledgments

The authors wish to thank Professors Antonio Laface and Vasudevan Srinivas for answering their questions. They also thank Osamu Fujino, Atsushi Ito and Ching-Jui Lai for careful reading of this manuscript and for helpful comments. They are grateful to Shinnosuke Okawa, Akiyoshi Sannai and Taro Sano for valuable conversations.

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Authors and Affiliations

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

    Yoshinori Gongyo & Shunsuke Takagi

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  1. Yoshinori Gongyo
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  2. Shunsuke Takagi
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Correspondence to Shunsuke Takagi.

Additional information

Dedicated to Professor Robert Lazarsfeld on the occasion of his 60th birthday.

Y. Gongyo was partially supported by Research expense from the JRF fund and by the Grand-in-Aid for Research Activity Start-Up \(\#\)24840009 and for Young Scientists (A) \(\#\)26707002 from JSPS. S. Takagi was partially supported by Grant-in-Aid for Young Scientists (B) \(\#\)23740024 and for Scientific Research (C) \(\#\)26400039 from JSPS. This material is based upon work supported by the National Science Foundation under Grant No. 0932078 000, while S. Takagi was in residence at the Mathematical Science Research Institute in Berkeley, California, during the spring semester 2013 of the program Commutative Algebra.

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Gongyo, Y., Takagi, S. Surfaces of globally F-regular and F-split type. Math. Ann. 364, 841–855 (2016). https://doi.org/10.1007/s00208-015-1238-4

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