# THE ARTINIAN QUOTIENT OF CODIMENSION n + 1

Shin, Yong-Su

• Accepted : 2019.08.13
• Published : 2019.08.31
• 24 3

#### 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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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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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.
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