Journal of the
Korean Mathematical Society JKMS

We find the Hilbert function and the minimal free resolution of a star-configuration in ${\mathbb P}^n$. The conditions are provided under which the Hilbert function of a star-configuration in ${\mathbb P}^2$ is generic or non-generic. We also prove that if ${\mathbb X}$ and $\mathbb Y$ are linear star-configurations in $\mathbb P^2$ of types $t$ and $s$, respectively, with $s\ge t\ge 3$, then the Artinian $k$-algebra $R/(I_\mathbb X+I_\mathbb Y)$ has the weak Lefschetz property.

Keywords: Hilbert functions, Artinian algebras, minimal free resolutions, weak Lefschetz property, star-configurations

MSC numbers: Primary 13P40; Secondary 14M10