Towards Common Zeros of Iterated Morphisms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915071641255936 |
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| author | Noytaptim, Chatchai Zhong, Xiao |
| author_facet | Noytaptim, Chatchai Zhong, Xiao |
| contents | Recently, the authors have proved the finiteness of common zeros of two iterated rational maps under some compositional independence assumptions. In this article, we advance towards a question of Hsia and Tucker on a Zariski non-density of common zeros of iterated morphisms on a variety. More precisely, we provide an affirmative answer in the case of Hénon type maps on $\mathbb{A}^2$, endomorphisms on $(\mathbb{P}^1)^n$, and polynomial skew products on $\mathbb{A}^2$ defined over $\overline{\mathbb{Q}}$. As a by-product, we prove a Tits' alternative analogy for semigroups generated by two regular polynomial skew products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15141 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards Common Zeros of Iterated Morphisms Noytaptim, Chatchai Zhong, Xiao Algebraic Geometry Dynamical Systems Number Theory 37P05, 37P30, 37P50 Recently, the authors have proved the finiteness of common zeros of two iterated rational maps under some compositional independence assumptions. In this article, we advance towards a question of Hsia and Tucker on a Zariski non-density of common zeros of iterated morphisms on a variety. More precisely, we provide an affirmative answer in the case of Hénon type maps on $\mathbb{A}^2$, endomorphisms on $(\mathbb{P}^1)^n$, and polynomial skew products on $\mathbb{A}^2$ defined over $\overline{\mathbb{Q}}$. As a by-product, we prove a Tits' alternative analogy for semigroups generated by two regular polynomial skew products. |
| title | Towards Common Zeros of Iterated Morphisms |
| topic | Algebraic Geometry Dynamical Systems Number Theory 37P05, 37P30, 37P50 |
| url | https://arxiv.org/abs/2412.15141 |