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http://dx.doi.org/10.4134/JKMS.2012.49.2.405

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)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.2, 2012 , pp. 405-417 More about this Journal
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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