Resurgence and Castelnuovo-Mumford regularity of certain monomial curves in ${\mathbb{A}}^3$

Abstract

Let $\mathfrak{p}$ be the defining ideal of the monomial curve $\mathcal{C}(2q+1,2q+1+m,2q+1+2m)$ in the affine space ${\mathbb{A}}_k^3$ parameterized by $(x^{2q+1},x^{2q+1+m},x^{2q+1+2m})$ where $gcd(2q+1,m)=1$. In this paper we compute the resurgence of $\mathfrak{p}$, the Waldschmidt constant of $\mathfrak{p}$ and the Castelnuovo-Mumford regularity of the symbolic powers of $\mathfrak{p}$.

To appear in AMV

References in corpus (1)

• Resurgences for ideals of special point configurations in ${\mathbf{P}}^N$ coming from hyperplane arrangements