Brill-Noether Loci and the Gonality Stratification of Mg
Gavril Farkas
Abstract
A Brill-Noether locus is a subvariety of Mg consisting of curves having certain linear series grd. We study the relative position of Brill-Noether loci with respect to the gonality stratification of Mg. We construct smooth curves in Pr 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.
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