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

  • Ahn, Jea-Man ;
  • Shin, Yong-Su
  • 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.

Keywords

Hilbert functions;Artinian algebras;minimal free resolutions;weak Lefschetz property;star-configurations

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