Title: Measures of Irrationality for Very General Abelian Varieties
Speaker: Olivier Martin
Speaker Info: Univ. of Chicago
Brief Description:
Special Note:
Abstract:
In recent years renewed attention has been brought to measures of irrationality for projective varieties. While vector bundle methods have been leveraged by Bastianelli, de Poi, Ein, Lazarsfeld, and Ullery to study the degree of irrationality and covering gonality of high degree hypersurfaces, Voisin has used the Chow group of zero-cycles to show that the covering gonality of a very general abelian variety of dimension g goes to infinity with g. I will discuss these recent developments and show how one can generalize Voisin's method in order to prove the following conjecture: A very general abelian variety of dimension at least 2k-1 has covering gonality greater than k. If time permits, I will explain how this method can be used to obtain new lower bounds on the degree of irrationality of abelian varieties.Date: Thursday, March 14, 2019