for a projective variety x and an ample divisor h on it, an h-polar cylinder in x is an open ruled affine subset whose complement is a support of an effective q-divisor q-rationally equivalent to h. this notion links together affine, birational and kahler geometries. i will show how to prove existence and non-existence of h-polar cylinders in smooth and mildly singular del pezzo surfaces (for different polarizations). the obstructions comes from log canonical thresholds and fujita numbers. as an application, i will answer an old question of zaidenberg and flenner about additive group actions on the cubic fermat affine threefold cone. this is a joint work with jihun park (postech) and joonyeong won (kaist).