The minimal log discrepancies on a smooth surface in positive characteristic

Abstract

This paper shows that Mustaţǎ–Nakamura’s conjecture holds for pairs consisting of a smooth surface and a multiideal with a real exponent over the base field of positive characteristic. As corollaries, we obtain the ascending chain condition of the minimal log discrepancies and of the log canonical thresholds for those pairs. We also obtain finiteness of the set of the minimal log discrepancies of those pairs for a fixed real exponent.

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Acknowledgements

The author expresses her hearty thanks to Kohsuke Shibata for his insightful comments which improves the paper. She also would like to thank Masayuki Kawakita, Lawrence Ein and Mircea Mustaţǎ for the useful discussions. A big part of these discussions was done during the author’s stay in MSRI (Program: Birational Geometry and Moduli Theory) and she is grateful for the support of MSRI. The author would like to thank the referee for useful comments to improve the paper.

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Correspondence to Shihoko Ishii.

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S. Ishii: The author is partially supported by JSPS 19K03428.

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Ishii, S. The minimal log discrepancies on a smooth surface in positive characteristic. Math. Z. 297, 389–397 (2021). https://doi.org/10.1007/s00209-020-02514-8

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