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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 |
Appears in Collections: | Staff Publications Elements |
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