Asian Journal of Mathematics
Volume 22 (2018)
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
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