English

Max Noether Theorem for Singular Curves

Algebraic Geometry 2022-02-21 v1

Abstract

Max Noether's Theorem asserts that if ω\omega is the dualizing sheaf of a nonsingular nonhyperelliptic projective curve, then the natural morphisms SymnH0(ω)H0(ωn)\text{Sym}^nH^0(\omega)\to H^0(\omega^n) are surjective for all n1n\geq 1. The result was extended for Gorenstein curves by many different authors in distinct ways. More recently, it was proved for curves with projectively normal canonical models, and curves whose non-Gorenstein points are bibranch at worse. Based on those works, we address the combinatorics of the general case and extend the result for any integral curve.

Keywords

Cite

@article{arxiv.2202.09349,
  title  = {Max Noether Theorem for Singular Curves},
  author = {Edson Martins Gagliardi and Renato Vidal Martins},
  journal= {arXiv preprint arXiv:2202.09349},
  year   = {2022}
}
R2 v1 2026-06-24T09:45:00.190Z