Asian Journal of Mathematics

Volume 22 (2018)

Number 3

Special issue in honor of Ngaiming Mok (2 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

Periodic subvarieties of a projective variety under the action of a maximal rank abelian group of positive entropy

Pages: 451 – 476



Fei Hu (Department of Mathematics, National University of Singapore; and Department of Mathematics, University of British Columbia, Vancouver, Canada)

Sheng-Li Tan (Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China)

De-Qi Zhang (Department of Mathematics, National University of Singapore)


We determine positive-dimensional $G$-periodic proper subvarieties of an $n$-dimensional normal projective variety $X$ under the action of an abelian group $G$ of maximal rank $n-1$ and of positive entropy. The motivation of the paper is to understand the obstruction for $X$ to be $G$-equivariant birational to the quotient variety of an abelian variety modulo the action of a finite group.


automorphism, complex dynamics, iteration, topological entropy

2010 Mathematics Subject Classification

14J50, 32H50, 32M05, 37B40

The first author was supported by a research assistantship of the NUS. The second author was supported by the NSFC and the Science Foundation of Shanghai (No. 13DZ2260400). The third author was supported by an ARF of the NUS.

Received 10 April 2016

Accepted 24 November 2017

Published 8 August 2018