January, 2025 Accumulation points on 3-fold canonical thresholds
Jheng-Jie CHEN
Author Affiliations +
J. Math. Soc. Japan Advance Publication 1-19 (January, 2025). DOI: 10.2969/jmsj/91509150

Abstract

Let k2 be a given integer. We study the set of 3-fold canonical thresholds ct(X;S) with 1k<ct(X;S)<1k1 where S is a Q-Cartier prime divisor of a projective 3-fold X. Express ct(X;S) as the rational number am where a (resp. m) denotes the weighted discrepancy (resp. weighted multiplicity). We conclude that if a54k4, then we may choose positive integers p and q satisfying ct(X;S)=am=1k+qp and q<6k3. As a consequence, the set of accumulation points of the set of 3-fold canonical thresholds consists of {0}{1k}kZ2. Moreover, we generalize the ACC for the set of 3-fold canonical thresholds to pairs.

Funding Statement

The author was partially supported by NCTS and National Science and Technology Council of Taiwan (Grant Numbers: 112-2115-M-008-006-MY2 and 113-2123-M-002-019-).

Citation

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Jheng-Jie CHEN. "Accumulation points on 3-fold canonical thresholds." J. Math. Soc. Japan Advance Publication 1 - 19, January, 2025. https://doi.org/10.2969/jmsj/91509150

Information

Received: 2 June 2023; Published: January, 2025
First available in Project Euclid: 8 January 2025

Digital Object Identifier: 10.2969/jmsj/91509150

Subjects:
Primary: 14E08
Secondary: 14E30 , 14J17

Keywords: 3-fold canonical thresholds , ACC of generalized pairs , accumulation points

Rights: Copyright ©2025 Mathematical Society of Japan

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