Tabes Bridges : The Kodaira Dimension of $M_g$ or: What to do when geometers go off the deep end

Posted by Tabes Bridges , part of the Graduate Algebraic Geometry Seminar.

At

Sept. 16, 2015, 3 p.m.

In

SEO 712

Abstract

I will review the basics of the geometry of the moduli space of stable curves $\overline{M}_g$, in particular its Picard group and its relation to the Picard group of the moduli stack $\overline{\mathcal{M}}_g$. I will then briefly discuss some classical results on the birational geometry for small $g$ before sketching the proof of the Eisenbud-Harris-Mumford Thereom that $M_g$ is of general type for $g\geq 23$. Along the way we will explore techniques for protecting oneself when "general" arguments become too much for some people.