Brill-Noether Loci and the Gonality Stratification of $M_g$

Abstract

A Brill-Noether locus is a subvariety of M_g consisting of curves having certain linear series g^r_d. We study the relative position of Brill-Noether loci with respect to the gonality stratification of M_g. We construct smooth curves in P^r of given degree and genus and having the `expected' gonality. As an application we give a new proof of our result about the Kodaira dimension of the moduli space of curves of genus 23.

arXiv comment14 pages, latex. Revised version as it will appear in Crelles Journal