Affine Surfaces which Contain the Affine Plane
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 nonisomorphic choices of Y. Our aim is to describe how to construct and classify these surfaces, as well as explain some of their properties.