Max Noether's Theorem for Integral Curves

2014/03/17 by Lia Feital Fusaro Abrantes, Abrantes, Lia Feital Fusaro, André Contiero +3 · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1403.4167

openalex publication_date 2014/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize, for integral curves, a celebrated result of Max Noether on global sections of the n-dualizing sheaf of a smooth nonhyperelliptic curve. This is our main result. We also obtain an embedding of a non-Gorenstein curve in a way that we can express the dimensions of the components of the ideal in terms of the main invariants of the curve. Afterwards we focus on gonality, Clifford index and Koszul cohomology of non-Gorenstein curves by allowing torsion free sheaves of rank 1 in their definitions. We find an upper bound for the gonality, which agrees with Brill-Noether's one for a rational and unibranch curve. We characterize curves of genus 5 with Clifford index 1, and, finally, we study Green's Conjecture for a certain class of curves, called nearly Gorenstein.

Citations

• green's canonical syzygy conjecture for generic curves of odd genus

Cited by

• On Enriques-Babbage Theorem for singular curves
• On Clifford dimension for singular curves

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