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Algebra Seminar

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.

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