# Algebraic Geometry Seminar

#### On Rational Varieties of Small Degree

**Speaker:**
Davide Fusi, Ohio State University

**Location:**
Warren Weaver Hall 1314

**Date:**
Tuesday, November 17, 2015, 3:30 p.m.

**Synopsis:**

Let X be a complex projective variety. Properties of special families of rational curves capture the geometry of X. In 2006 Ionescu and Russo gave a criterion that describes rationality in terms of suitable families of rational curves through a point of X. Inspired by their result we prove a stronger version of the criterion, namely we give necessary and sufficient conditions for the local ring of X at a point x to be C-isomorphic to the local ring of a point of the projective space. As an application we define a degree of rationality in a natural way and we provide a classification result for small values.