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THE ARTINIAN QUOTIENT OF CODIMENSION n + 1

Shin, Yong-Su

  • Received : 2019.06.27
  • Accepted : 2019.08.13
  • Published : 2019.08.31

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

Hilbert function;star configuration;generic Hilbert function;weak Lefschetz property;strong Lefschetz property

References

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  2. E. Carlini, E. Guardo & A. Van Tuyl: Star configurations on generic hypersurfaces. J. Algebra 407 (2014) 1-20.
  3. A.V. Geramita, B. Harbourne & J.C. Migliore: Star Configurations in ${\mathbb{P}}^n$. J. Algebra 376 (2013), 279-299.
  4. Y.R. Kim & Y.S. Shin: The Artinian Point Star Configuration Quotient and the Strong Lefschetz Property. In prepartation.
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  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

Acknowledgement

Supported by : Sungshin Women's University