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

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

2000-07-05

arxiv.org/abs/math/0007024v2

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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