# Cylinders in del Pezzo surfaces

## Ivan Cheltsov (Edinburgh)

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. 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). 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 and Joonyeong Won.

Tuesday, April 28th, at 4:00pm in HBH 227

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