# Algebraic Geometry Seminar

#### Picard Groups of Hurwitz Spaces

**Speaker:**
Anand Deopurkar, Columbia University

**Location:**
Warren Weaver Hall 201

**Date:**
Tuesday, April 7, 2015, 3:30 p.m.

**Synopsis:**

Hurwitz spaces are the moduli spaces of branched covers of the projective line. Although they have been studied classically, many questions about their geometry are still unanswered. In this talk, I will address one such question--the question of their Picard group. It is conjectured that (modulo torsion) the Picard group is spanned by certain tautological divisors. I will relate this conjecture to an analogous statement about the moduli space of curves and sketch a proof for Hurwitz spaces of covers of degree up to five. This is joint work with Anand Patel.