Arithmetic degree and its application to Zariski dense orbit conjecture
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912544752402432 |
|---|---|
| author | Matsuzawa, Yohsuke Xie, Junyi |
| author_facet | Matsuzawa, Yohsuke Xie, Junyi |
| contents | We prove that for a dominant rational self-map $f$ on a quasi-projective variety defined over $\overline{\mathbb{Q}}$, there is a point whose $f$-orbit is well-defined and its arithmetic degree is arbitrarily close to the first dynamical degree of $f$. As an application, we prove that Zariski dense orbit conjecture holds for a birational map defined over $\overline{\mathbb{Q}}$ whose first dynamical degree is strictly larger than its third dynamical degree. In particular, the conjecture holds for birational maps on threefolds whose first dynamical is degree greater than $1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06160 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic degree and its application to Zariski dense orbit conjecture Matsuzawa, Yohsuke Xie, Junyi Algebraic Geometry Dynamical Systems Number Theory 37P15, 37P55 We prove that for a dominant rational self-map $f$ on a quasi-projective variety defined over $\overline{\mathbb{Q}}$, there is a point whose $f$-orbit is well-defined and its arithmetic degree is arbitrarily close to the first dynamical degree of $f$. As an application, we prove that Zariski dense orbit conjecture holds for a birational map defined over $\overline{\mathbb{Q}}$ whose first dynamical degree is strictly larger than its third dynamical degree. In particular, the conjecture holds for birational maps on threefolds whose first dynamical is degree greater than $1$. |
| title | Arithmetic degree and its application to Zariski dense orbit conjecture |
| topic | Algebraic Geometry Dynamical Systems Number Theory 37P15, 37P55 |
| url | https://arxiv.org/abs/2409.06160 |