Brill--Noether theory over the Hurwitz space

Abstract: Let $C$ be a curve of genus $g$. A fundamental problem in the theory of algebraic curves is to understand maps of $C$ to projective space of dimension r of degree d. When the curve $C$ is general, the moduli space of such maps is well-understood by the main theorems of Brill-Noether theory. However, in nature, curves $C$ are often encountered already equipped with a map to some projective space, which may force them to be special in moduli. The simplest case is when $C$ is general among curves of fixed gonality. Despite much study over the past three decades, a similarly complete picture has proved elusive in this case. In this talk, I will discuss recent joint work with Eric Larson and Isabel Vogt that completes such a picture, by proving analogs of all of the main theorems of Brill--Noether theory in this setting.

algebraic geometry

Audience: researchers in the topic

Comments: The discussion for Hannah Larson’s talk is taking place not in zoom-chat, but at tinyurl.com/2020-08-21-hl (and will be deleted after 3-7 days).

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com