Cylinders in singular del Pezzo surfaces

Abstract

For each del Pezzo surface S with du Val singularities, we determine whether it admits a (KS)-polar cylinder or not. If it allows one, then we present an eective Q-divisor D that is Q-linearly equivalent to KS and such that the open set SnSupp(D) is a cylinder. As a corollary, we classify all the del Pezzo surfaces with du Val singularities that admit non-trivial Ga-actions on their ane cones dened by their anticanonical divisors. (c) Foundation Compositio Mathematica 2016.