Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE MINIMAL GRADED FREE RESOLUTION OF THE UNION OF TWO STAR CONFIGURATIONS IN 𝕡n AND THE WEAK LEFSCHETZ PROPERTY

  • Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
  • Received : 2017.08.15
  • Accepted : 2017.09.26
  • Published : 2017.11.15
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Abstract

We find a graded minimal free resolution of the union of two star configurations ${\mathbb{X}}$ and ${\mathbb{Y}}$ (not necessarily linear star configurations) in ${\mathbb{P}}^n$ of type s and t for s, $t{\geq}2$, and $n{\geq}3$. As an application, we prove that an Artinian ring $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ of two linear star configurations ${\mathbb{X}}$ and ${\mathbb{Y}}$ in ${\mathbb{P}}^3$ of type s and t has the weak Lefschetz property for $s{\geq}{\lfloor}\frac{1}{2}(^t_2){\rfloor}$ and $t{\geq}2$.

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References

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