Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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AN ARTINIAN POINT-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)
  • Received : 2017.01.07
  • Accepted : 2018.03.27
  • Published : 2018.07.01
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Abstract

In this paper, we study an Artinian point-configuration quotient having the SLP. We show that an Artinian quotient of points in $\mathbb{p}^n$ has the SLP when the union of two sets of points has a specific Hilbert function. As an application, we prove that an Artinian linear star configuration quotient $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP if $\mathbb{X}$ and $\mathbb{Y}$ are linear starconfigurations in $\mathbb{p}^2$ of type s and t for $s{\geq}(^t_2)-1$ and $t{\geq}3$. We also show that an Artinian $\mathbb{k}$-configuration quotient $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP if $\mathbb{X}$ is a $\mathbb{k}$-configuration of type (1, 2) or (1, 2, 3) in $\mathbb{p}^2$, and $\mathbb{X}{\cup}\mathbb{Y}$ is a basic configuration in $\mathbb{p}^2$.

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Acknowledgement

Supported by : NRF (Korea)

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