Back to Algebraic Geometry Seminar: Fall 2013
Algebraic Geometry Seminar
Date: Tuesday, Nov 5, 2013
Time: 3:30PM - 4:30PM
Location: LCB 225
Steffen Marcus
University of Utah
Title |
A geometric perspective on the piecewise polynomiality of double Hurwitz numbers |
Abstract |
Hurwitz numbers count degree d branched covers of the Riemann sphere by a genus g Riemann surface with prescribed ramification over one branch point and simple ramification over the others. They are intimately related to the geometry of the moduli space of curves through the famous ELSV formula. Double Hurwitz numbers similarly count covers with prescribed ramification over two points. In this talk I’m going to explain how we can describe double Hurwitz numbers as intersection numbers on the moduli space of curves using the geometry of the moduli space of relative stable maps. This helps explains geometrically the chamber/wall-crossing piecewise polynomial structure of double Hurwitz numbers. This is joint work with Renzo Cavalieri. |
Algebraic Geometry