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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.
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참고문헌 (31)
참고문헌 신청
안재만 / 2012 / THE MINIMAL FREE RESOLUTION OF A STAR-CONFIGURATION IN Pn AND THE WEAK LEFSCHETZ PROPERTY / 대한수학회지 49(2):405~417
C. Bocci / 2010 / Comparing powers and symbolic powers of ideals / J. Alge-braic Geom 19(3):399~417
C. Bocci / 2010 / The resurgence of ideals of points and the containment problem / Proc. Amer. Math. Soc 138(4):1175~1190
E. Carlini / 2014 / Star configurations on generic hypersurfaces / J. Algebra 407:1~20
M. V. Catalisano / Secant varieties to the varieties of reducible hypersurfaces in Pn / J. Algebra
C. Bocci / 2010 / Comparing powers and symbolic powers of ideals / J. Alge-braic Geom 19(3):399~417
C. Bocci / 2010 / The resurgence of ideals of points and the containment problem / Proc. Amer. Math. Soc 138(4):1175~1190
E. Carlini / 2014 / Star configurations on generic hypersurfaces / J. Algebra 407:1~20
M. V. Catalisano / Secant varieties to the varieties of reducible hypersurfaces in Pn / J. Algebra
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