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

Robert Friedman

Columbia University

November 18, 2014

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.