Cylindricity of weighted singular del Pezzo surfaces over fields of characteristic zero

Abstract

In this paper, we study the cylindricity of $\mathbb{k}$-forms of singular del Pezzo surfaces obtained by blowing up weighted projective planes $\mathbb{P}(1,1,m)$ over an arbitrary field $\mathbb{k}$ of characteristic zero. As an application, we obtain vertical cylinders on higher-dimensional fibrations whose generic fibers are such $\mathbb{k}$-forms.

26 pages, 2 figures; v3: minor changes; revised Introduction; added reference; Comments welcome!