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SOME APPLICATION OF THE UNION OF TWO π•œ-CONFIGURATIONS IN β„™2

  • Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
  • Received : 2014.03.26
  • Accepted : 2014.06.30
  • Published : 2014.08.15
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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].

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References

  1. 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. https://doi.org/10.1142/S1005386714000121
  2. A. V. Geramita, T. Harima, and Y. S. Shin. Extremal point sets and Gorenstein ideals, Adv. Math. 152 (2000), no. 1, 78-119. https://doi.org/10.1006/aima.1998.1889
  3. 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. https://doi.org/10.1006/jabr.1998.7651
  4. Y. S. Shin, Secants to The Variety of Completely Reducible Forms and The Union of Star-Configurations, J. of Algebra and its Applications 11 (2012), no. 6, 1250109 (27 pages). https://doi.org/10.1142/S0219498812501095
  5. 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. https://doi.org/10.14403/jcms.2012.25.3.553
  6. Y. S. Shin, Some Examples of The Union of Two Linear Star-configurations in $\mathbb{P}^2$ Having Generic Hilbert Function, J. of the Chungcheong Math. Soc. 26 (2013), no. 2, 403-409. https://doi.org/10.14403/jcms.2013.26.2.403

Cited by

  1. AN ARTINIAN POINT-CONFIGURATION QUOTIENT AND THE STRONG LEFSCHETZ PROPERTY vol.55, pp.4, 2014, https://doi.org/10.4134/jkms.j170035