Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/234647
Title: Surjective endomorphisms of projective surfaces -- the existence of infinitely many dense orbits
Authors: Jia, Jia
Xie, Junyi
Zhang, De-Qi 
Keywords: math.AG
math.AG
math.DS
math.NT
14J50, 32H50, 37B40, 08A35
Issue Date: 8-May-2020
Citation: Jia, Jia, Xie, Junyi, Zhang, De-Qi (2020-05-08). Surjective endomorphisms of projective surfaces -- the existence of infinitely many dense orbits. ScholarBank@NUS Repository.
Abstract: Let $f \colon X \to X$ be a surjective endomorphism of a normal projective surface. When $\operatorname{deg} f \geq 2$, applying an (iteration of) $f$-equivariant minimal model program (EMMP), we determine the geometric structure of $X$. Using this, we extend the second author's result to singular surfaces to the extent that either $X$ has an $f$-invariant non-constant rational function, or $f$ has infinitely many Zariski-dense forward orbits; this result is also extended to Adelic topology (which is finer than Zariski topology).
URI: https://scholarbank.nus.edu.sg/handle/10635/234647
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