Семинар НУЛ АГП «Cylinders, flexibility, and quadrics»

Given an algebraic variety X, by a cylinder in X we mean an open subset isomorphic to the product A¹ x Z for some affine variety Z. We discuss a connection between cylinders and G_a-actions on affine varieties and provide a criterion of flexibility of an affine variety in terms of cylinders. We prove flexibility of two families of affine varieties: the complement of a quadric in a projective space and an affine cone over a smooth complete intersection of two quadrics in a projective space. The talk is based on a joint work with Hoang Le Truong.