Regularity bounds for curves by minimal generators and Hilbert function

Cioffi, Francesca; Marinari, Maria Grazia; Ramella, Luciana

Regularity bounds for curves by minimal generators and Hilbert function

Authors

Cioffi, Francesca

Marinari, Maria Grazia

Ramella, Luciana

Description

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.
9 pages