Max Noether Theorem for Singular Curves

2022/02/18 by Gagliardi, Edson Martins, Martins, Renato Vidal · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.09349

Abstract

Max Noether's Theorem asserts that if ω is the dualizing sheaf of a nonsingular nonhyperelliptic projective curve, then the natural morphisms SymⁿH⁰(ω)→ H⁰(ωⁿ) are surjective for all n≥ 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.

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