Browse > Article
http://dx.doi.org/10.14403/jcms.2017.30.4.435

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)
Publication Information
Journal of the Chungcheong Mathematical Society / v.30, no.4, 2017 , pp. 435-443 More about this Journal
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 $t{\geq}2$.
Keywords
Hilbert functions; star configurations; minimal graded free resolution; the weak Lefschetz property;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 C. Bocci and B. Harbourne, Comparing powers and symbolic powers of ideals, J. Algebraic Geom. 19 (2010), no. 3, 399-417.   DOI
2 M. V. Catalisano, A. V. Geramita, A. Gimigliano, and Y. S. Shin, The Secant Line Variety to the Varieties of Reducible Plane Curves, Annali di Matematica (2016) 195:423-443.   DOI
3 M. V. Catalisano, A. V. Geramita, A. Gimigliano, B. Habourne, J. Migliore, U. Nagel, and Y. S. Shin, Secant Varieties to the Varieties of Reducible Hypersurfaces in ${\mathbb{P}^n}$, J. of Alg. Geo. submitted.
4 A. V. Geramita, T. Harima, and Y. S. Shin, Extremal point setsand Gorenstein ideals, Adv. Math. 152 (2000), no. 1, 78-119.   DOI
5 A. V. Geramita, J. C. Migliore, and S. Sabourin, On the first infinitesimal neighborhood of a linear configuration of points in ${\mathbb{P}^2}$, J. of Alg. 298, (2008), 563-611.
6 A. V. Geramita, B. Harbourne, and J. C. Migliore, Star Configurations in ${\mathbb{P}^n}$, J. Algebra, 376 (2013) 279-299.   DOI
7 Y. R. Kim and Y. S. Shin, Star-configurations in ${\mathbb{P}^n}$ and The weak Lefschetz Property, Comm. Alg. 44 (2016), 3853-3873.   DOI
8 J. P. Park and Y. S. Shin, The Minimal Free Resolution of A Star-configuration in ${\mathbb{P}^n}$, J. Pure Appl. Algebra. 219 (2015), 2124-2133.   DOI
9 Y. S. Shin, Star-Configurations in ${\mathbb{P}^2}$ Having Generic Hilbert Functions and The weak Lefschetz Property, Comm. in Algebra, 40 (2012), 2226-2242.   DOI
10 Y. S. Shin, Some Application of the Union of Two ${\mathbb{k}}$-configurations in ${\mathbb{P}^2}$, J. of Chungcheong Math. Soc. 27 (2014), no. 3, 413-418.
11 Y. S. Shin, The minimal free resolution of the union of two linear star-configurations in ${\mathbb{P}^2}$, Comm. in Korean Math. Soc. 31 (2016), no. 4, 683-693.   DOI
12 R. Stanley, Weyl groups, the hard Lefschetz theorem, and the Sperner property, SIAM J. Algebraic Discrete Methods 1, (1980), 168-184.   DOI