Cylinders in del Pezzo fibrations
Résumé
We show that a del Pezzo fibration $π: V \rightarrow W$ of degree d contains a vertical open cylinder, that is, an open subset whose intersection with the generic fiber of $π$ is isomorphic to $Z\times\mathbb{A}_{K}^{1}$ for some quasi-projective variety $Z$ defined over the function field $K$ of $W$ , if and only if $d \ge 5$ and $π: V \rightarrow W$ admits a rational section. We also construct twisted cylinders in total spaces of threefold del Pezzo fibrations $π: V \rightarrow P^1$ of degree $d \le 4$.
Domaines
Géométrie algébrique [math.AG]Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...