SFU Number Theory and Algebraic Geometry Seminar: Jake Levinson

A basic question about an algebraic variety X is how similar it is to projective space. One measure of similarity is the minimum degree of a rational map from X to projective space, the "degree of irrationality". This number, not to mention the corresponding minimal-degree maps, is in general challenging to compute, but captures special features of the geometry of X. I will discuss some recent joint work with David Stapleton and Brooke Ullery on asymptotic bounds for degrees of irrationality of divisors X on projective varieties Y. Here, the minimal-degree rational maps $X \dashrightarrow \mathbb{P}^n$ turn out to "know" about Y and factor through rational maps $Y \dashrightarrow \mathbb{P}^n$ fibered in curves that are, in an appropriate sense, also of minimal degree.