Asian Journal of Mathematics

Volume 22 (2018)

Number 2

Special issue in honor of Ngaiming Mok (1 of 3)

Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University

On minimal $3$-folds of general type with maximal pluricanonical section index

Pages: 257 – 268



Meng Chen (School of Mathematical Sciences & Shanghai Centre for Mathematical Sciences, Fudan University, Shanghai, China)


Let $X$ be a minimal $3$-fold of general type. The pluricanonical section index $\delta (X)$ is defined to be the minimal integer $m$ so that $P_m (X) \geq 2$. According to Chen–Chen, one has either $1 \leq \delta (X) \leq 15$ or $\delta (X) = 18$. This note aims to intensively study those with maximal such index. A direct corollary is that the 57th canonical map of every minimal $3$-fold of general type is stably birational.


minimal threefolds of general type, pluricanonical section index, canonical stability index

2010 Mathematics Subject Classification

14E05, 14J30

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The author was supported by the National Natural Science Foundation of China (#11571076, #11231003, #11421061) and the Program of Shanghai Academic Researcher Leader (Grant no. 16XD1400400).

Received 17 April 2016

Accepted 2 June 2017

Published 15 June 2018