Affine Surfaces which Contain the Affine Plane

David Villalobos Paz, Princeton University
Fine Hall 110

We can consider the question: given an affine variety X, does there exist another affine variety Y of the same dimension which contains X as an open subset? When X is the complex affine line, no such Y exists, but already when X is the complex affine plane, there are infinitely many non-isomorphic choices of Y. Our aim is to describe how to construct and classify these surfaces, as well as explain some of their properties.