Seminars & Colloquia Calendar
Low degree points on curves
Isabel Vogt -- MIT
Location: Hill 525
Date & time: Wednesday, 07 November 2018 at 2:00PM - 3:00PM
Abstract: We will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris-Silverman and Abramovich-Harris, it is understood when this invariant is 1, 2, or 3; by work of Debarre-Fahlaoui these criteria do not generalize to e at least 4. We will focus on scenarios under which we can guarantee that this invariant is actually equal to the gonality using the auxiliary geometry of a surface containing the curve.
This is joint work with Geoffrey Smith.