Algebraic Geometry Seminar
Hannah Larson
Stanford University
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.
Monday September 16, 2019 at 4:00 PM in 427 SEO