Apr 12 2021

Algebraic Geometry Seminar: Brill–Noether theory over the Hurwitz space, by Hannah Larson

April 12, 2021

3:00 PM - 3:50 PM




Chicago, IL

Hannah Larson (Stanford University): Brill--Noether theory over the Hurwitz space

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 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.

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Izzet Coskun

Date posted

Mar 5, 2021

Date updated

Mar 5, 2021


Hannah Larson | (Stanford University)