A dynamical characterisation of smooth cubic affine surfaces of Markov type
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917138122407936 |
|---|---|
| author | Abboud, Marc |
| author_facet | Abboud, Marc |
| contents | Using valuative techniques, we show that a smooth affine surface with a non-elementary automorphism group and completable by a cycle of rational curves is either the algebraic torus or a smooth cubic affine surface of Markov type. Furthermore we show that smooth cubic affine surfaces of Markov type do no admit dominant endomorphisms which are not automorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A dynamical characterisation of smooth cubic affine surfaces of Markov type Abboud, Marc Algebraic Geometry Complex Variables Dynamical Systems 37F10, 37F80, 13A18, 37P99 Using valuative techniques, we show that a smooth affine surface with a non-elementary automorphism group and completable by a cycle of rational curves is either the algebraic torus or a smooth cubic affine surface of Markov type. Furthermore we show that smooth cubic affine surfaces of Markov type do no admit dominant endomorphisms which are not automorphisms. |
| title | A dynamical characterisation of smooth cubic affine surfaces of Markov type |
| topic | Algebraic Geometry Complex Variables Dynamical Systems 37F10, 37F80, 13A18, 37P99 |
| url | https://arxiv.org/abs/2512.10455 |