Regularity bounds for curves by minimal generators and Hilbert function

Francesca Cioffi; Maria Grazia Marinari; Luciana Ramella

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Regularity bounds for curves by minimal generators and Hilbert function

Francesca Cioffi·Maria Grazia Marinari·Luciana Ramella

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Abstract

Let $ρ_C$ be the regularity of the Hilbert function of a projective curve $C$ in $\mathbb P^n_K$ over an algebraically closed field $K$ and $α_1,...,α_{n-1}$ be minimal degrees for which there exists a complete intersection of type $(α_1,...,α_{n-1})$ containing the curve $C$. Then the Castelnuovo-Mumford regularity of $C$ is upper bounded by $\max\{ρ_C+1,α_1+...+α_{n-1}-(n-2)\}$. We study and, for space curves, refine the above bound providing several examples.

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BibTeX RIS

Francesca Cioffi, Maria Grazia Marinari, Luciana Ramella. 2006-02-02. Regularity bounds for curves by minimal generators and Hilbert function. https://arxiv.org/abs/math/0507583

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