On the structure of open del Pezzo surfaces
| Autor: | Palka, Karol, Pełka, Tomasz |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $(X,D)$ be an open log del Pezzo surface of rank one, that is, $X$ is a normal projective surface of Picard rank one, and the boundary $D$ is a reduced, nonzero divisor on $X$. We show that, up to well described exceptions in characteristics 2, 3 and 5, the open part $X\setminus D$ admits an $\mathbb{A}^1$- or $\mathbb{A}^1_*$-fibration with no base points on the boundary of the minimal log resolution of $(X,D)$. In characteristic 0, this improves a well-known structure theorem of Miyanishi-Tsunoda. Within the proof, we classify rational anti-canonical curves contained in smooth loci of canonical del Pezzo surfaces of rank one. Comment: 38 pages; 10 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|