Polarized cylinders in Du Val del Pezzo surfaces of degree two

Abstract

Let $S$ be a del Pezzo surface with at worst Du Val singularities of degree $2$ such that $S$ admits an $(-K_S)$-polar cylinder. In this article, we construct an $H$-polar cylinder for any ample $\mathbb{Q}$-divisor $H$ on $S$.

31 pages, 10 figures; v3: Add Figure 10 and Table 2 in the final section. Some gaps and typos are corrected. To appear in Transformation Groups