# Algebraic Geometry Seminar

#### Low degree points on curves

**Speaker:**
Isabel Vogt, MIT

**Location:**
Warren Weaver Hall 317

**Date:**
Tuesday, November 6, 2018, 3:30 p.m.

**Synopsis:**

In this talk 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 devote particular attention to 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.