Tabes Bridges : Moduli Spaces of Curves or: Geometric Legos

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

At

Oct. 15, 2014, 2 p.m.

In

SEO 712

Abstract

The moduli space of smooth algebraic curves (a.k.a. compact Riemann surfaces) $M_g$ and its variants are objects of central interest in algebraic geometry, topology, combinatorics, and mathematical physics. I will describe the basic topological structure (in particular, Riemann's famous parameter count), state some of what is known (e.g. concerning the birational geometry of such spaces), and attempt to give a brief taste of the divisor class theory on $\overline{M}_{g,n}$, the moduli space of stable genus-$g$ curves with $n$ marked points.