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

Title & Authors
THE MINIMAL FREE RESOLUTION OF A STAR-CONFIGURATION IN ?n AND THE WEAK LEFSCHETZ PROPERTY
Ahn, Jea-Man; Shin, Yong-Su;

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