# THE MINIMAL FREE RESOLUTION OF A STAR-CONFIGURATION IN ?n AND THE WEAK LEFSCHETZ PROPERTY

• Ahn, Jea-Man (Department of Mathematics Education Kongju National University) ;
• Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
• Received : 2011.03.10
• Published : 2012.03.01

#### Abstract

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 $s{\geq}t{\geq}3$, then the Artinian k-algebra $R/(I_{\mathbb{X}}+I_{\mathbb{Y})$ has the weak Lefschetz property.

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