On the Castelnuovo-Mumford regularity of connected curves

2003/09/02 by Daniel Giaimo, Giaimo, Daniel
Computer Science · Mathematics · #13D02 #14H99 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:13D02 #msc:14H99

paper · pdf · doi:10.48550/arxiv.math/0309051

21 pages, 2 figures

arxiv created 2003/09/02 · openalex publication_date 2003/09/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove the Eisenbud-Goto conjecture for connected curves. We also investigate the structure of connected curves for which this bound is optimal. In particular, we construct connected curves of arbitrarily high degree in projective 4-space having maximal regularity, but no extremal secants. We also show that any connected curve in projective 3-space of degree at least 5 that has no linear components and has maximal regularity has an extremal secant.

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