# Algebra Seminar

Date:

09/25/2019 - 2:00pm to 3:00pm

Location:

745 POT

Speaker(s) / Presenter(s):

Hannah Larson, Stanford University

Title: A refined Brill-Noether theory over Hurwitz spaces

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.

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