David Jensen, September 24th, 2013

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.