Cylinders in singular del Pezzo surfaces. (21st April 2016) - Cheltsov, Ivan
Abstract : For each del Pezzo surface $S$ with du Val singularities, we determine whether it admits a $(-K_{S})$ -polar cylinder or not. If it allows one, then we present an effective $\mathbb{Q}$ -divisor $D$ that is $\mathbb{Q}$ -linearly equivalent to $-K_{S}$ and such that the open set $S\setminus \text{Supp}(D)$ is a cylinder. As a corollary, we classify all the del Pezzo surfaces with du Val singularities that admit non-trivial $\mathbb{G}_{a}$ -actions on their affine cones defined by their anticanonical divisors.