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In this paper, we study an Artinian point-configuration quotient having the SLP. We show that an Artinian quotient of points in $\P^n$ 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 $R/(I_\X+I_\Y)$ has the SLP if $\X$ and $\Y$ are linear star-configurations in $\P^2$ of type $s$ and $t$ for $s\ge \binom{t}{2}-1$ and $t\ge 3$. We also show that an Artinian $\k$-configuration quotient $R/(I_\X+I_\Y)$ has the SLP if $\X$ is a $\k$-configuration of type $(1,2)$ or $(1,2,3)$ in $\P^2$, and $\X\cup\Y$ is a basic configuration in $\P^2$.
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참고문헌 (22)
참고문헌 신청
안재만 / 2012 / THE MINIMAL FREE RESOLUTION OF A STAR-CONFIGURATION IN Pn AND THE WEAK LEFSCHETZ PROPERTY / 대한수학회지 49(2):405~417
E. Carlini / 2014 / Star configurations on generic hypersurfaces / J. Algebra 407:1~20
E. Carlini / 2011 / Star configuration points and generic plane curves / Proc. Amer. Math. Soc. 139(12):4181~4192
M. V. Catalisano / Secant varieties to the varieties of reducible hypersurfaces in ${\mathbb{P}^n}$ / J. of Alg. Geo.
M. V. Catalisano / 2016 / The secant line variety to the varieties of reducible plane curves / Ann. Mat. Pura Appl. 195(2):423~443
E. Carlini / 2014 / Star configurations on generic hypersurfaces / J. Algebra 407:1~20
E. Carlini / 2011 / Star configuration points and generic plane curves / Proc. Amer. Math. Soc. 139(12):4181~4192
M. V. Catalisano / Secant varieties to the varieties of reducible hypersurfaces in
M. V. Catalisano / 2016 / The secant line variety to the varieties of reducible plane curves / Ann. Mat. Pura Appl. 195(2):423~443
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