Regularity bounds for curves by minimal generators and Hilbert function

2005/07/28 by Francesca Cioffi, Cioffi, Francesca, Maria Grazia Marinari +3
Computer Science · Mathematics · #14F17 #14H50 #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:14F17 #msc:14H50

paper · pdf · doi:10.48550/arxiv.math/0507583

9 pages

openalex publication_date 2005/07/28 · arxiv created 2006/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ρ_C be the regularity of the Hilbert function of a projective curve C in \mathbb Pⁿ_K over an algebraically closed field K and α₁,...,α_n-1 be minimal degrees for which there exists a complete intersection of type (α₁,...,α_n-1) containing the curve C. Then the Castelnuovo-Mumford regularity of C is upper bounded by max\ρ_C+1,α₁+...+α_n-1-(n-2)\. We study and, for space curves, refine the above bound providing several examples.

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