# Algebraic Geometry Seminar

#### On the Effective Cone of the Moduli Space of Pointed Rational Curves

**Speaker:**
David Jensen , Yale University

**Location:**
Warren Weaver Hall 317

**Date:**
Tuesday, September 24, 2013, 3:30 p.m.

**Synopsis:**

Recent years have witnessed a flurry of activity concerning the effective cones of moduli spaces, particularly the space M_{0,n} parameterizing rational curves with marked points. Early in this study, it was noticed by Keel and Vermeire that each of the boundary divisors of M_{0,n} generates an extremal ray of the effective cone, but that these do not account for all of the extremal rays. More recently, the Keel-Vermeire construction was vastly generalized by Castravet and Tevelev to produce a large class of new extremal rays, and they conjectured that these are all. We will discuss further progress on these questions. This is joint work with Brent Doran and Noah Giansiracusa.