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A GRADED MINIMAL FREE RESOLUTION OF THE m-TH ORDER SYMBOLIC POWER OF A STAR CONFIGURATION IN ℙn

  • Park, Jung Pil (Faculty of Liberal Education Seoul National University) ;
  • Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
  • Received : 2019.11.05
  • Accepted : 2020.12.09
  • Published : 2021.03.01

Abstract

In [30] the author finds a graded minimal free resolution of the 2-nd order symbolic power of a star configuration in ℙn of any codimension r. In this paper, we find that of any m-th order symbolic power of a star configuration in ℙn of codimension 2, which generalizes the result of Galetto, Geramita, Shin, and Van Tuyl in [15, Theorem 5.3]. Furthermore, we extend it to the m-th order symbolic power of a star configuration in ℙn of any codimension r for m = 3, 4, which also generalizes the result of Biermann et al. in [1, Corollaries 4.6 and 5.7]. We also suggest how to find a graded minimal free resolution of the m-th order symbolic power of a star configuration in ℙn of any codimension r for m ≥ 5.