Session S35 - Moduli Spaces in Algebraic Geometry and Applications

Wednesday, July 14, 14:40 ~ 15:20 UTC-3

Brill--Noether theory over the Hurwitz space

Isabel Vogt

University of Washington/Brown University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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 Hannah Larson that completes such a picture, by proving analogs of all of the main theorems of Brill--Noether theory in this setting.

Joint work with Eric Larson (University of Washington/Brown University) and Hannah Larson (Stanford University).

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