April, 2024 On generalized minimal log discrepancy
Weichung CHEN, Yoshinori GONGYO, Yusuke NAKAMURA
Author Affiliations +
J. Math. Soc. Japan 76(2): 393-449 (April, 2024). DOI: 10.2969/jmsj/90119011


We discuss the ACC conjecture and the LSC conjecture for minimal log discrepancies of generalized pairs. We prove that some known results on these two conjectures for usual pairs are still valid for generalized pairs. We also discuss the theory of complements for generalized pairs.

Funding Statement

The first author was supported by Japan-Taiwan exchange association as a student of the University of Tokyo, by the University of Tokyo as a project researcher, and by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2019-1614) when he was working at the Steklov International Mathematical Center. The second author was partially supported by JSPS KAKENHI No. 15H03611, 16H02141, 17H02831, 18H01108, and JPJSBP120219935. The third author is partially supported by JSPS KAKENHI No. 18K13384, 16H02141, 17H02831, 18H01108, and JPJSBP120219935.


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Weichung CHEN. Yoshinori GONGYO. Yusuke NAKAMURA. "On generalized minimal log discrepancy." J. Math. Soc. Japan 76 (2) 393 - 449, April, 2024. https://doi.org/10.2969/jmsj/90119011


Received: 19 August 2022; Published: April, 2024
First available in Project Euclid: 24 January 2024

Digital Object Identifier: 10.2969/jmsj/90119011

Primary: 14E30
Secondary: 14B05

Keywords: ACC conjecture , generalized pair , LSC conjecture , minimal log discrepancy

Rights: Copyright ©2024 Mathematical Society of Japan


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Vol.76 • No. 2 • April, 2024
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