# Algebraic Geometry Seminar

#### Cylinders in Del Pezzo Surfaces

**Speaker:**
Ivan Cheltsov, University of Edinburgh

**Location:**
Warren Weaver Hall 201

**Date:**
Tuesday, February 3, 2015, 3:30 p.m.

**Synopsis:**

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 Kähler 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 come 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 joint work with Jihun Park (POSTECH) and Joonyeong Won (KAIST).