Back to Algebraic Geometry Seminar: Spring 2015
Algebraic Geometry Seminar
Date: Tuesday, Jan 27, 2015
Time: 3:30PM - 4:30PM
Location: LCB 215
Nicola Tarasca
University of Utah
Title |
Pointed Castelnuovo numbers |
Abstract |
The classical Castelnuovo numbers count linear series of minimal degree and fixed dimension on a general curve, in the case when this number is finite. For pencils, that is, linear series of dimension one, the Castelnuovo specialize to the better known Catalan numbers. In this talk, I will present a formula for the number of linear series on a general curve with prescribed ramification at an arbitrary point, when the expected number is finite. As an application, I will show how to solve certain enumerative problems on moduli spaces of curves, and how to obtain improved bounds for the slope of the cone of effective divisor classes on symmetric products of a general curve. This is a joint work with Gavril Farkas. |
Algebraic Geometry