Colloquium
3:00 p.m., Monday
Math Annex 1100
Gavril Farkas
University of Michigan
The Global Geometry of the Moduli Space of Curves
The guiding problem of algebraic geometry is to classify
algebraic varieties up to isomorphism. In dimension 1 this
problem is approached by considering the moduli space of curves
(Riemann surfaces) of genus g. This space which is the universal
parameter space for curves of genus g, is playing an increasingly
important role in algebraic and arithmetic geometry as well as
string theory.
I will review basic properties of the moduli space of curves
and describe several fundamental problems related to its Kodaira
dimension and cone of curves. I will also discuss recent work
leading to a counterexample to the HarrisMorrisson Slope Conjecture
on effective divisors on the moduli space of curves.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
