关于主导有理自映射在射影簇上周期点和前周期点高度有界的性质
On the height boundedness of periodic and preperiodic points of dominant rational self-maps on projective varieties
AI总结：
本文推翻了关于周期点高度有界的猜想，并证明了在射影簇上某些主导有理自映射的周期点集高度有界，同时指出前周期点可能不满足这一性质。
摘要：
我们给出一个反例，推翻了以下猜想：在仿射空间上度数至少为二的自同构的孤立周期点集是一个有界高度的集合。作为积极的结果，我们证明了任何在射影簇上 cohomologically 超几何的主导有理自映射，都存在一个非空的 Zariski 开集，其上周期点集的高度是有界的。关于前周期点，我们给出一个例子，表明相同的陈述可能不成立。
英文摘要：
We give a counterexample to the following conjecture: the set of isolated periodic points of an automorphism of degree at least two on an affine space is a set of bounded height. As a positive result, we prove that any cohomologically hyperbolic dominant rational self-map on a projective variety admits a non-empty Zariski open subset on which the set of periodic points is height bounded. Concerning preperiodic points, we give an example suggesting that the same statement may fail.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
