Speaker: Angela Gibney.
Title: A Conjectural Description of the Ample Divisors on the Moduli Space of Curves.
Affiliation: University of Michigan.
Date: Tuesday, January 21, 2003.
Place and Time: Room 102 - Love Building, 3:35-4:30 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.

Abstract. The moduli space M(g,n) of stable, n-pointed curves of genus g is an important object of study in many areas of mathematics and even physics. This is largely because many questions about curves can be translated into questions about the birational geometry of the moduli space. One very effective way to learn about the birational geometry of a variety is to study its ample divisors.
    A divisor in the moduli space of curves is conjecturally ample if and only if it positvely intersects a class of smooth, rational curves called F-curves. I will describe the F-curves and explain why they are thought to specify all effective curves on M(g,n). I will also discuss the surprising fact that if the conjecture is true for M(0,g+n) then it is true for M(g,n) as well as the current state of knowledge about the conjecture.