School Seminars and Colloquia

Log minimal model program for \(M_g\)

Algebra/Geometry/Topology Seminar

by David Smyth

Institution: Australian National University
Date: Fri 15th March 2013
Time: 3:15 PM
Location: 213 Richard Berry

Abstract: The Deligne-Mumford compactification of the moduli space of Riemann surfaces is one of the key technical tools of algebraic geometry. We will describe recent progress on a long-term program to construct and understand new geometric compactifications of the moduli space of Riemann surfaces. Conjecturally, these compactifications should fit together in the so-called log minimal model program for the moduli space of curves. While this program is very far from completion, I will describe what happens in the special case of \(M_{1,n}\) - the moduli space of pointed elliptic curves - in order to illustrate some of the beautiful geometry associated with these new compactifications