Minimal degree fibrations in curves and asymptotic degrees of irrationality

Abstract: 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.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

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