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http://dx.doi.org/10.4134/JKMS.j180258

THE ARTINIAN POINT STAR CONFIGURATION QUOTIENT AND THE STRONG LEFSCHETZ PROPERTY  

Kim, Young-Rock (Major in Mathematics Education Graduate School of Education Hankuk University of Foreign Studies)
Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
Publication Information
Journal of the Korean Mathematical Society / v.56, no.3, 2019 , pp. 645-667 More about this Journal
Abstract
It has been little known when an Artinian point quotient has the strong Lefschetz property. In this paper, we find the Artinian point star configuration quotient having the strong Lefschetz property. We prove that if ${\mathbb{X}}$ is a star configuration in ${\mathbb{P}}^2$ of type s defined by forms (a-quadratic forms and (s - a)-linear forms) and ${\mathbb{Y}}$ is a star configuration in ${\mathbb{P}}^2$ of type t defined by forms (b-quadratic forms and (t - b)-linear forms) for $b=deg({\mathbb{X}})$ or $deg({\mathbb{X}})-1$, then the Artinian ring $R/(I{\mathbb_{X}}+I{\mathbb_{Y}})$ has the strong Lefschetz property. We also show that if ${\mathbb{X}}$ is a set of (n+ 1)-general points in ${\mathbb{P}}^n$, then the Artinian quotient A of a coordinate ring of ${\mathbb{X}}$ has the strong Lefschetz property.
Keywords
Hilbert functions; generic Hilbert functions; star configurations; linear star configurations;
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