An Artinian point-configuration quotient and the strong Lefschetz property
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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 $\P^2$.
Abstract
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 $\P^2$.
참고문헌 (22)
- 안재만, "THE MINIMAL FREE RESOLUTION OF A STAR-CONFIGURATION IN Pn AND THE WEAK LEFSCHETZ PROPERTY", 대한수학회지, 49(2), pp.405~417 (2012), 대한수학회
- E. Carlini, "Star configurations on generic hypersurfaces", J. Algebra, 407, pp.1~20 (2014)[DOI]
- E. Carlini, "Star configuration points and generic plane curves", Proc. Amer. Math. Soc., 139(12), pp.4181~4192 (2011)[DOI]
- M. V. Catalisano, "Secant varieties to the varieties of reducible hypersurfaces in <TEX>${\mathbb{P}^n}$<", TEX>, ~
- M. V. Catalisano, "The secant line variety to the varieties of reducible plane curves", Ann. Mat. Pura Appl., 195(2), pp.423~443 (2016)[DOI]
- A. V. Geramita, "Star configurations in <TEX>${\mathbb{P}^n}$<", TEX>, 2013, pp.376, 279~299
- A. V. Geramita, "Matroid configurations and symbolic powers of their ideals", ~
- A. V. Geramita, "The Hilbert function of a level algebra", Mem. Amer. Math. Soc., 186(872), pp.vi+139~ (2007)
- A. V. Geramita, "Extremal point sets and Gorenstein ideals", Adv. Math., 152(1), pp.78~119 (2000)[DOI]
- A. V. Geramita, "On the first infinitesimal neighborhood of a linear configuration of points in <TEX>${\mathbb{P}^2}$<", TEX>, 2006, pp.298(2), 563~611
- A. V. Geramita, "k-configurations in <TEX>${\mathbb{P}^3}$<", TEX> all have extremal resolutions, 1999, pp.213(1), 351~368
- T. Harima, "Some examples of unimodal Gorenstein sequences", J. Pure Appl. Algebra, 103(3), pp.313~324 (1995)[DOI]
- T. Harima, "The Lefschetz Properties, Lecture Notes in Mathematics, 2080" (2013), Springer
- T. Harima, "The weak and strong Lefschetz properties for Artinian K-algebras", J. Algebra, 262(1), pp.99~126 (2003)[DOI]
- Y. R. Kim, "Star-configurations in <TEX>${\mathbb{P}^n}$<", TEX> and the weak-Lefschetz property, 2016, pp.44(9), 3853~3873
- J. Migliore, "Ideals of general forms and the ubiquity of the weak Lefschetz property", J. Pure Appl. Algebra, 182(1), pp.79~107 (2003)[DOI]
- "Proc. Amer. Math. Soc.", 2018, 507~523
- J. Migliore, "Survey article: a tour of the weak and strong Lefschetz properties", J. Commut. Algebra, 5(3), pp.329~358 (2013)[DOI]
- J. P. Park, "The minimal free graded resolution of a star-configuration in <TEX>${\mathbb{P}^n}$<", TEX>, 2015, pp.219(6), 2124~2133
- Y. S. Shin, "Secants to the variety of completely reducible forms and the Hilbert function of the union of star-configurations", J. Algebra Appl., 11(6), pp.27~ (2012)
- Y. S. Shin, "Star-configurations in <TEX>${\mathbb{P}^2}$<", TEX> having generic Hilbert function and the weak Lefschetz property, 2012, pp.40(6), 2226~2242
- 신용수, "SOME APPLICATION OF THE UNION OF TWO k-CONFIGURATIONS IN P2", 충청수학회지, 27(3), pp.413~418 (2014), 충청수학회[DOI]