English

Brill-Noether loci in codimension two

Algebraic Geometry 2013-02-21 v2

Abstract

Let us consider the locus in the moduli space of curves of genus 2k defined by curves with a pencil of degree k. Since the Brill-Noether number is equal to -2, such a locus has codimension two. Using the method of test surfaces, we compute the class of its closure in the moduli space of stable curves.

Keywords

Cite

@article{arxiv.1201.4948,
  title  = {Brill-Noether loci in codimension two},
  author = {Nicola Tarasca},
  journal= {arXiv preprint arXiv:1201.4948},
  year   = {2013}
}

Comments

v2: new section 7, the main Theorem is now proved for ALL k>=3. Final version to appear in Compositio Mathematica. This version is slightly different

R2 v1 2026-06-21T20:08:52.265Z