Houston's Online Home for Country Legends!

### Now Playing

Country Legends 97.1FM
Houston's Online Home ...

# Algebraic Geometry Seminar: A Decomposition of Hurwitz Space

##### Where

Rice University
6100 Main
Houston, TX 77005

##### Upcoming

4:00 p.m. Tuesday, Nov. 27, 2012

##### Categories

Events,  Learning,  On Campus | Alumni

In this talk we will describe a natural decomposition of the Hurwitz space $\mathcal{H}_{d,g}$ parametrizing simply-branched covers of $\mathbb{P}^1$. By studying the geometry of this decomposition, we will deduce the irreducibility of the Gieseker-Petri locus $\mathcal{GP}^1_{d} \subset \mathcal{M}_{g}$ where $d = \frac{g+2}{2}$. Furthermore, we will explain the role this decomposition plays in establishing upper bounds for slopes of sweeping curves in the $d$-gonal locus.