Hannah Larson : A refined Brill-Noether theory over Hurwitz spaces

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Sept. 16, 2019, 4 p.m.

In

427 SEO

Abstract

The Brill-Noether theorem describes the maps of general curves to projective space. Recently, the Brill-Noether theory of general k-gonal curves C has gathered much interest: Coppens-Martens exhibited components of the Brill-Noether loci W^r_d(C) with different dimensions; work of Pflueger and Jensen-Ranganathan determined the dimension of the largest component. In this talk, I will introduce a natural refinement of Brill-Noether loci for curves with a distinguished map C --> P^1, using the splitting type of push forwards of line bundles to P^1. In particular, studying this refinement determines the dimensions of all irreducible components of W^r_d(C) for general k-gonal C.