English

On nondegeneracy of curves

Algebraic Geometry 2008-04-11 v2 Combinatorics

Abstract

A curve is called nondegenerate if it can be modeled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We show that up to genus 4, every curve is nondegenerate. We also prove that the locus of nondegenerate curves inside the moduli space of curves of fixed genus g > 1 is min(2g+1,3g-3)-dimensional, except in case g=7 where it is 16-dimensional.

Keywords

Cite

@article{arxiv.0802.0420,
  title  = {On nondegeneracy of curves},
  author = {Wouter Castryck and John Voight},
  journal= {arXiv preprint arXiv:0802.0420},
  year   = {2008}
}
R2 v1 2026-06-21T10:09:20.113Z