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 geometrynumber theory

Audience: researchers in the topic

Comments: There is a pre-talk by Eric Larson on limit linear series.

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MAGIC (Michigan - Arithmetic Geometry Initiative - Columbia)

Series comments: Description: Research seminar in arithmetic geometry

(Zoom password = order of the alternating group on six letters)

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