Rational self-maps of projective surfaces with a regular iterate
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909936279093248 |
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| author | Saleh, Sina |
| author_facet | Saleh, Sina |
| contents | We show that if $Φ: X \dashrightarrow X$ is a dominant rational self-map of a projective surface $X$ over $\mathbb{C}$ with a regular and non-invertible iterate $Φ^n$, then we can take $n \leq 12$. This bound is sharp and realized on $X = \mathbb{P}^2$. In the case where $Φ$ is a birational self-map of $\mathbb{P}^2$ we prove that as long as $Φ$ does not preserve a non-constant fibration, if some iterate $Φ^n$ is regular then $Φ$ itself must be regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational self-maps of projective surfaces with a regular iterate Saleh, Sina Algebraic Geometry Dynamical Systems We show that if $Φ: X \dashrightarrow X$ is a dominant rational self-map of a projective surface $X$ over $\mathbb{C}$ with a regular and non-invertible iterate $Φ^n$, then we can take $n \leq 12$. This bound is sharp and realized on $X = \mathbb{P}^2$. In the case where $Φ$ is a birational self-map of $\mathbb{P}^2$ we prove that as long as $Φ$ does not preserve a non-constant fibration, if some iterate $Φ^n$ is regular then $Φ$ itself must be regular. |
| title | Rational self-maps of projective surfaces with a regular iterate |
| topic | Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2509.05194 |