Communications of the Korean Mathematical Society (대한수학회논문집)

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THE MINIMAL FREE RESOLUTION OF THE UNION OF TWO LINEAR STAR-CONFIGURATIONS IN ℙ2

  • Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
  • Received : 2015.11.14
  • Published : 2016.10.31
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Abstract

In [1], the authors proved that the finite union of linear star-configurations in $\mathbb{P}^2$ has a generic Hilbert function. In this paper, we find the minimal graded free resolution of the union of two linear star-configurations in $\mathbb{P}^2$ of type $s{\times}t$ with $\(^t_2\){\leq}s$ and $3{\leq}t$.

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References

  1. J. Ahn and Y. S. Shin, The union of linear star-configurations in ${\mathbb{p}}^2$ and the weak-Lefschetz property, In Preparation.
  2. J. Ahn and Y. S. Shin, The minimal free resolution of a star-configuration in ${\mathbb{p}}^n$ and the weak-Lefschetz property, J. Korean Math. Soc. 49 (2012), no. 2, 405-417. https://doi.org/10.4134/JKMS.2012.49.2.405
  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. Alg. Geo. submitted.
  4. A. V. Geramita, B. Harbourne, and J. C. Migliore, Star configurations in ${\mathbb{p}}^n$, J. Algebra 376 (2013), 279-299. https://doi.org/10.1016/j.jalgebra.2012.11.034
  5. A. V. Geramita and P. Marocia, The ideal of forms vanishing at a finite set of points in ${\mathbb{p}}^n$, J. Algebra 90 (1984), no. 2, 528-555. https://doi.org/10.1016/0021-8693(84)90188-1
  6. 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. Algebra 298 (2006), no. 2, 563-611. https://doi.org/10.1016/j.jalgebra.2006.01.035
  7. A. Geramita and F. Orecchia, Minimally generating ideals defining certain tangent cones, J. Algebra 78 (1982), no. 1, 36-57. https://doi.org/10.1016/0021-8693(82)90101-6
  8. Y. R. Kim and Y. S. Shin, Star-configurations in ${\mathbb{p}}^n$ and the weak-Lefschetz property, Comm. Alg. to appear.
  9. J. P. Park and Y. S. Shin, The minimal free graded resolution of a star-configuration in ${\mathbb{p}}^n$, J. Pure Appl. Algebra. 219 (2015), no. 6, 2124-2133. https://doi.org/10.1016/j.jpaa.2014.07.026
  10. Y. S. Shin, Secants to the variety of completely reducible forms and the union of star-configurations, J. Algebra Appl. 11 (2012), no. 6, 1250109, 27 pp.
  11. Y. S. Shin, Star-configurations in ${\mathbb{p}}^2$ having generic Hilbert functions and the weak-Lefschetz property, Comm. Algebra 40 (2012), no. 6, 2226-2242. https://doi.org/10.1080/00927872.2012.656783