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The minimal free resolution of the union of two linear star-configurations in $\P^2$

Yong Su Shin
대한수학회 (The Korean Mathematical Society)|2016.10|대한수학회논문집 (Communications of the KMS)|제31권 제4호|pp. 683-693

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참고문헌

키워드

minimal graded free resolutionHilbert functiongeneric Hilbert functionstar-configurations
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초록

In \cite{AGS:1}, the authors proved that the finiteunion of linear star-configurations in $\P^2$ has a generic Hilbert function. In this paper, we find the minimal graded free resolution of the union of two linear star-configurations in $\P^2$ of type $s\times t$ with $\binom{t}{2}\le s$ and $3\le t$.

Abstract

In \cite{AGS:1}, the authors proved that the finiteunion of linear star-configurations in $\P^2$ has a generic Hilbert function. In this paper, we find the minimal graded free resolution of the union of two linear star-configurations in $\P^2$ of type $s\times t$ with $\binom{t}{2}\le s$ and $3\le t$.

참고문헌 (11)

  1. J. Ahn, "The union of linear star-configurations in P2 and the weak-Lefschetz property", ~
  2. 안재만, "THE MINIMAL FREE RESOLUTION OF A STAR-CONFIGURATION IN Pn AND THE WEAK LEFSCHETZ PROPERTY", 대한수학회지, 49(2), pp.405~417 (2012), 대한수학회
  3. M. V. Catalisano, "Secant varieties to the varieties of reducible hypersurfaces in Pn", J. Alg. Geo
  4. A. V. Geramita, "Star configurations in Pn", J. Algebra, 376, pp.279~299 (2013)
  5. A. V. Geramita, "The ideal of forms vanishing at a finite set of points in Pn", J. Algebra, 90(2), pp.528~555 (1984)
  6. A. V. Geramita, "On the first infinitesimal neighborhood of a linear configuration of points in P2", J. Algebra, 298(2), pp.563~611 (2006)
  7. A. Geramita, "Minimally generating ideals defining certain tangent cones", J. Algebra, 78(1), pp.36~57 (1982)
  8. Y. R. Kim, "Star-configurations in Pn and the weak-Lefschetz property", Comm. Alg
  9. J. P. Park, "The minimal free graded resolution of a star-configuration in Pn", J. Pure Appl. Algebra, 219(6), pp.2124~2133 (2015)
  10. Y. S. Shin, "Secants to the variety of completely reducible forms and the union of star-configurations", J. Algebra Appl, 11(6), pp.27~ (2012)
  11. Y. S. Shin, "Star-configurations in P2 having generic Hilbert functions and the weak-Lefschetz property", Comm. Algebra, 40(6), pp.2226~2242 (2012)

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