# Algebra Seminar

Title: Components of Brill-Noether Loci for Curves with Fixed Gonality

Abstract: The geometry of an algebraic curve is intimately related to the theory of linear systems of special divisors defined on that curve, and the study of such divisors is known as Brill-Noether theory. A sequence of results in the 80's, the seminal being the Brill-Noether Theorem, concerns the geometry of Brill-Noether varieties for a curve C that is general in the moduli space M_g of smooth, projective curves of genus g. Recently, there has been a surge of interest when C is general in the Hurwitz space H_g,k parameterizing smooth, projective curves of genus g equipped with a prescribed degree k branched cover of the projective line. In this talk we will aim to present a generalization of the Brill-Noether Theorem to this more general setting that extends results of Pfleuger and Jensen-Ranganathan by extending their analysis of certain families of tableaux. This talk is based on joint work with Dave Jensen.