Back to Algebraic Geometry Seminar: Spring 2016
Algebraic Geometry Seminar
Date: Tuesday, Mar 8, 2016
Time: 3:30PM - 4:30PM
Location: JFB 102
Brooke Ullery
University of Utah
Title |
Measures of irrationality for hypersurfaces of large degree |
Abstract |
The gonality of a smooth projective curve is the smallest degree of a map from the curve to the projective line. There are a few different definitions that attempt to generalize the notion of gonality to higher dimensional varieties. The intuition is that the higher these numbers, the further the variety is from being rational. I will discuss some of these definitions, and present joint work with Lawrence Ein and Rob Lazarsfeld. Our main result is that if X is an n-dimensional hypersurface of degree d at least 5/2 n, then any dominant rational map from X to P^n must have degree at least d-1. |
Algebraic Geometry