Back to Algebraic Geometry Seminar: Fall 2013
Algebraic Geometry Seminar
Date: Tuesday, Sep 3, 2013
Time: 3:30PM - 4:30PM
Location: LCB 225
Nicola Tarasca
University of Utah
Title |
Brill-Noether loci in moduli spaces of curves |
Abstract |
A classical way of producing subvarieties of the moduli space of curves is by means of Brill-Noether theory: the locus in the moduli space of curves of genus g consisting of curves with a pencil of degree k has codimension g-2k+2. While Brill-Noether divisors have been extensively studied, little is known about higher codimension Brill-Noether loci. In this talk I will focus on the locus in the moduli space of curves of genus 2k defined by curves with a pencil of degree k. This is a locus of codimension two. Using the method of test surfaces, I will show how to produce a closed formula for the class of its closure in the moduli space of stable curves. |
Algebraic Geometry