On the dynamics of endomorphisms of affine surfaces
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909094684655616 |
|---|---|
| author | Abboud, Marc |
| author_facet | Abboud, Marc |
| contents | In [FJ07], Favre and Jonsson developed tools from valuative theory to study the dynamics of a dominant endomorphism of the complex affine plane. We extend this theory to the case of any affine surface, over any field. We give a new method to construct an eigenvaluation of an endomorphism. We generalize the result of Favre and Jonsson and show that the first dynamical degree of a dominant endomorphism of anormal affine surface is an algebraic integer of degree at most 2. Plus, we obtain a new result of rigidity. The set of first dynamical degrees of loxodromic automorphisms of a given affine surface must be contained in the set of integers or in the set of algebraic numbers of degree 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18381 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the dynamics of endomorphisms of affine surfaces Abboud, Marc Algebraic Geometry Dynamical Systems In [FJ07], Favre and Jonsson developed tools from valuative theory to study the dynamics of a dominant endomorphism of the complex affine plane. We extend this theory to the case of any affine surface, over any field. We give a new method to construct an eigenvaluation of an endomorphism. We generalize the result of Favre and Jonsson and show that the first dynamical degree of a dominant endomorphism of anormal affine surface is an algebraic integer of degree at most 2. Plus, we obtain a new result of rigidity. The set of first dynamical degrees of loxodromic automorphisms of a given affine surface must be contained in the set of integers or in the set of algebraic numbers of degree 2. |
| title | On the dynamics of endomorphisms of affine surfaces |
| topic | Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2311.18381 |