The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

THE ARTINIAN QUOTIENT OF CODIMENSION n + 1

  • Shin, Yong-Su (Department of Mathematics, Sungshin Women's University)
  • Received : 2019.06.27
  • Accepted : 2019.08.13
  • Published : 2019.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

We investigate all kinds of the Hilbert function of the Artinian quotient of the coordinate ring of a linear star configuration in ${\mathbb{P}}^n$ of type (n+1) (or (n+1)-general points in ${\mathbb{P}}^n$), which generalizes the result [7, Theorem 3.1].

Keywords

References

  1. J. Ahn & 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
  2. E. Carlini, E. Guardo & A. Van Tuyl: Star configurations on generic hypersurfaces. J. Algebra 407 (2014) 1-20. https://doi.org/10.1016/j.jalgebra.2014.02.013
  3. A.V. Geramita, B. Harbourne & 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
  4. Y.R. Kim & Y.S. Shin: The Artinian Point Star Configuration Quotient and the Strong Lefschetz Property. In prepartation.
  5. J.P. Park & Y.S. Shin: The Minimal Free Resolution of a Star-configuration in ${\mathbb{P}}^n$. J. Pure Appl. Algebra 219 (2015), 2124-2133. https://doi.org/10.1016/j.jpaa.2014.07.026
  6. Y.S. Shin: Some Examples of the Union of Two Linear Star-configurations in ${\mathbb{P}}^2$ Having Generic Hilbert Function. J. Chungcheong Math. Soc. 26 (2013), no. 2, 403-409. https://doi.org/10.14403/jcms.2013.26.2.403
  7. Y.S. Shin: The Hilbert function of the Artinian quotient of codimension 3. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 25 (2018), no. 4, 337-343