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

DOI: https://dx.doi.org/10.4310/AJM.2018.v22.n2.a3

Author

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

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

14E05, 14J30

Full Text (PDF format)

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