Cylindrical ample divisors on Du Val del Pezzo surfaces

Abstract The existence of polarized cylinders in normal projective varieties corresponds to admitting non-trivial ???? a {\mathbb{G}_{a}} -action on their affine cones defined by the polarized pairs. Note that a criterion for polarized cylinders in smooth del Pezzo surfaces is studied. Hence, we observe the existing condition of polarized cylinders in del Pezzo surfaces with at worst Du Val singularities. Let S be a del Pezzo surface with at worst Du Val singularities of degree ≥ 3 {\geq 3} . We then construct an H-polar cylinder for any ample ℚ {\mathbb{Q}} -divisor H on S.