Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/234643
 Title: Endomorphisms of quasi-projective varieties -- towards Zariski dense orbit and Kawaguchi-Silverman conjectures Authors: Jia, JiaShibata, Takahiro Xie, JunyiZhang, De-Qi Keywords: math.AGmath.AGmath.DSmath.NT14J50, 08A35, 32H50, 37B40 Issue Date: 12-Apr-2021 Citation: Jia, Jia, Shibata, Takahiro, Xie, Junyi, Zhang, De-Qi (2021-04-12). Endomorphisms of quasi-projective varieties -- towards Zariski dense orbit and Kawaguchi-Silverman conjectures. ScholarBank@NUS Repository. Abstract: Let $X$ be a quasi-projective variety and $f\colon X\to X$ a finite surjective endomorphism. We consider Zariski Dense Orbit Conjecture (ZDO), and Adelic Zariski Dense Orbit Conjecture (AZO). We consider also Kawaguchi-Silverman Conjecture (KSC) asserting that the (first) dynamical degree $d_1(f)$ of $f$ equals the arithmetic degree $\alpha_f(P)$ at a point $P$ having Zariski dense $f$-forward orbit. Assuming $X$ is a smooth affine surface, such that the log Kodaira dimension $\bar{\kappa}(X)$ is non-negative (resp. the \'etale fundamental group $\pi_1^{\text{\'et}}(X)$ is infinite), we confirm AZO, (hence) ZDO, and KSC (when $\operatorname{deg}(f)\geq 2$) (resp. AZO and hence ZDO). We also prove ZDO (resp. AZO and hence ZDO) for every surjective endomorphism on any projective variety with ''larger'' first dynamical degree (resp. every dominant endomorphism of any semiabelian variety). URI: https://scholarbank.nus.edu.sg/handle/10635/234643 Appears in Collections: Staff PublicationsElements

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