Tabes Bridges : The Brill-Noether Divisor on $\overline{\mathcal{M}}_g$, or: How to prove things about curves by playing favorites

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

At

Oct. 28, 2015, 3 p.m.

In

SEO 712

Abstract

In my talk a few weeks ago, I sketched the proof that $\mathcal{M}_g$ is of general type (i.e. maximal Kodaira dimension) modulo the major non-formal input, the computation of the class of the Brill-Noether divisor (which, by comparing, allows us to conclude that the canonical class is big). My goal today is to give a reasonably detailed overview of this calculation, and in doing so demonstrate many of the standard techniques for studying $\mathcal{M}_g$.