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http://dx.doi.org/10.14403/jcms.2014.27.3.413

SOME APPLICATION OF THE UNION OF TWO 𝕜-CONFIGURATIONS IN ℙ2  

Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.27, no.3, 2014 , pp. 413-418 More about this Journal
Abstract
It has been proved that the union of two linear star-configurations in $\mathbb{P}^2$ of type s and t for either $3{\leq}t{\leq}10$ or $\(\frac{t}{2}\)-1{\leq}s$ with $3{\leq}t$ has maximal Hilbert function. We extend the condition to $\[\frac{1}{2}\(\frac{t}{2}\)\]{\leq}s$, so that it is true for either $3{\leq}t{\leq}10$ or $\[\frac{1}{2}\(\frac{t}{2}\)\]{\leq}s$ with $3{\leq}t$, which extends the result of [6].
Keywords
Hilbert function; $\mathbb{k}$-configuration in $\mathbb{P}^2$; star-configuration in $\mathbb{P}^2$;
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Times Cited By KSCI : 2  (Citation Analysis)
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2 J. Ahn and Y. S. Shin. The Minimal Free Resolution of a Fat Star-Configuration in $\mathbb{P}^n$, Algebra Colloquium 21 (2014), no. 1, 157-166.   DOI
3 A. V. Geramita, T. Harima, and Y. S. Shin. Extremal point sets and Gorenstein ideals, Adv. Math. 152 (2000), no. 1, 78-119.   DOI   ScienceOn
4 Y. S. Shin, On the Hilbert Function of the Union of Two Linear Star-configurations in $\mathbb{P}^2$, J. of the Chungcheong Math. Soc. 25 (2012), no. 3, 553-562.   DOI
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6 A. V. Geramita and Y. S. Shin. $\mathbb{k}$-configurations in $\mathbb{P}^3$ All have extremal resolutions, J. Algebra 213 (1999), no. 1, 351-368.   DOI   ScienceOn