On the height boundedness of periodic and preperiodic points of dominant rational self-maps on projective varieties
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915849285140480 |
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| author | Matsuzawa, Yohsuke Sano, Kaoru |
| author_facet | Matsuzawa, Yohsuke Sano, Kaoru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09010 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the height boundedness of periodic and preperiodic points of dominant rational self-maps on projective varieties Matsuzawa, Yohsuke Sano, Kaoru Algebraic Geometry Dynamical Systems Number Theory 37P15, 37P55 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. |
| title | On the height boundedness of periodic and preperiodic points of dominant rational self-maps on projective varieties |
| topic | Algebraic Geometry Dynamical Systems Number Theory 37P15, 37P55 |
| url | https://arxiv.org/abs/2603.09010 |