Journal of the
Korean Mathematical Society JKMS

In \cite{GHM}, Geramita, Harbourne, and Migliore find a graded minimal free resolution of the $2$nd order symbolic power of the ideal of a linear star configuration in $\mathbb P^n$ of any codimension $r$. In \cite{GGSV}, Geramita, Galetto, Shin, and Van Tuyl extend the result on a general star configuration in $\mathbb P^n$ but for codimension $2$. In this paper, we find a graded minimal free resolution of the $2$nd order symbolic power of the ideal of a general star configuration in $\mathbb P^n$ of any codimension $r$ using a matroid configuration in \cite{GHMN}. This generalizes both the result on a {\em linear} star configuration in $\mathbb P^n$ of codimension $r$ in \cite{GHM} and the result on a general star configuration in $\mathbb P^n$ of {\em codimension $2$} in \cite{GGSV}.

Keywords: a graded minimal free resolution, symbolic powers, regular powers, star configurations

MSC numbers: 13A17, 14M05

Supported by: This research was supported by a grant from Sungshin Women’s University