# The geometry and topology of rational surfaces with an anticanonical cycle

 Topology of Algebraic Varieties Topic: The geometry and topology of rational surfaces with an anticanonical cycle Speaker: Robert Friedman Affiliation: Columbia University Date: Tuesday, November 18 Time/Room: 2:00pm - 3:00pm/S-101 Video Link: http://video.ias.edu/tav/2014/1118-RobertFriedman

Let $Y$ be a smooth rational surface and let $D$ be an effective divisor linearly equivalent to $-K_Y$, such that $D$ is a cycle of smooth rational curves. Such pairs $(Y,D)$ arise in many contexts, for example in the study of degenerations of $K3$ surfaces or in the theory of deformations of minimally elliptic singularities. Deformation types of such pairs come with two extra pieces of structure: the “generic” ample cone, i.e. the ample cone of a generic small deformation, and a distinguished set of divisor classes of square $-2$ orthogonal to the components of the cycle. The goal of this talk is to describe these structures as well as their applications to various questions involving geometric, topological and lattice-theoretic properties of such pairs.