Cylinders in del Pezzo surfaces

TL;DR

This paper investigates specific divisors on del Pezzo surfaces whose complements form affine line bundles over smooth affine curves, contributing to the understanding of the geometric structure of these surfaces.

Contribution

It introduces a classification of effective ample divisors on del Pezzo surfaces with complements that are affine line bundles, revealing new geometric properties.

Findings

Characterization of divisors with affine line bundle complements

Identification of conditions for the complements to be $A^1$-bundles

Insights into the structure of del Pezzo surfaces

Abstract

On del Pezzo surfaces, we study effective ample $\mathbb{R}$-divisors such that the complements of their supports are isomorphic to $\mathbb{A}^1$-bundles over smooth affine curves.