Back to Algebraic Geometry Seminar: Spring 2022
Algebraic Geometry Seminar
Date: Tuesday, Feb 1, 2022
Time: 3:30PM - 4:30PM
Location: See individual entries
Virtual
Sebastian Bozlee
Tufts University
Title |
A classification of Gorenstein compactifications of M_{1,n} |
Abstract |
The moduli space of pointed algebraic curves M_{g,n} of genus g is of fundamental interest in algebraic geometry. However, it is not compact, so one searches for compactifications of M_{g,n} which are themselves moduli spaces. Each such compactification is a richly interpretable birational model of M_{g,n}. In this talk we will present a new family of compactifications of M_{1,n} whose points parametrize Gorenstein curves coming from joint work with Adrian Neff and Bob Kuo. These new moduli spaces provably exhaust such Gorenstein modular compactifications of M_{1,n}, the first general classification of modular compactifications since 2012. Time permitting, we will explore the tropical and log geometric reasoning that led to the discovery of these spaces and our classification result. |
Algebraic Geometry