David Smyth : Modular Compactifications of M_{g,n}

Posted by , part of the Algebraic Geometry Seminar.

At

April 1, 2010, 4 p.m.

In

SEO 636

Abstract

A modular compactification of M_{g,n} is (roughly) a deformation-open class of singular curves with the property that every one-parameter family of smooth curves has a unique limit contained in that class. A modular compactification is stable if all the curves parametrized have the property that every rational component has three distinguished points. We will present a general classification of modular compactifications of M_{g,n} in terms of simple combinatorial data, which will include Schubert's moduli space of pseudostable curves and Hassett's spaces of weighted pointed stable curves as special cases.