On the effective cone of the moduli space of pointed rational curves

David Jensen, September 24th, 2013

Recent years have witnessed a flurry of activity concerning the effective cones of moduli
spaces, particularly the space M0,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 M0,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.