Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/234650
Title: Wild automorphisms of projective varieties, the maps which have no invariant proper subsets
Authors: Oguiso, Keiji
Zhang, De-Qi 
Keywords: math.AG
math.AG
math.DS
14J50, 32M05, 11G10
Issue Date: 11-Feb-2020
Citation: Oguiso, Keiji, Zhang, De-Qi (2020-02-11). Wild automorphisms of projective varieties, the maps which have no invariant proper subsets. ScholarBank@NUS Repository.
Abstract: Let $X$ be a projective variety and $\sigma$ a wild automorphism on $X$, i.e., whenever $\sigma(Z) = Z$ for a non-empty Zariski-closed subset $Z$ of $X$, we have $Z = X$. Then $X$ is conjectured to be an abelian variety with $\sigma$ of zero entropy (and proved to be so when ${\rm dim} \, X \le 2$) by Z. Reichstein, D. Rogalski and J. J. Zhang in their study of projectively simple rings. This conjecture has been generally open for more than a decade. In this note, we confirm this original conjecture when ${\rm dim} \, X \le 3$ and $X$ is not a Calabi-Yau threefold, and also show that $\sigma$ is of zero entropy when ${\rm dim} \, X \le 4$ and the Kodaira dimension $\kappa(X) \ge 0$.
URI: https://scholarbank.nus.edu.sg/handle/10635/234650
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