Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A POINT STAR-CONFIGURATION IN ℙn HAVING GENERIC HILBERT FUNCTION

  • Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
  • Received : 2014.10.31
  • Accepted : 2015.01.27
  • Published : 2015.02.15
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Abstract

We find a necessary and sufficient condition for which a point star-configuration in $\mathbb{P}^n$ has generic Hilbert function. More precisely, a point star-configuration in $\mathbb{P}^n$ defined by general forms of degrees $d_1,{\ldots},d_s$ with $3{\leq}n{\leq}s$ has generic Hilbert function if and only if $d_1={\cdots}=d_{s-1}=1$ and $d_s=1,2$. Otherwise, the Hilbert function of a point star-configuration in $\mathbb{P}^n$ is NEVER generic.

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References

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