A POINT STAR-CONFIGURATION IN Pn HAVING GENERIC HILBERT FUNCTION

Abstract

We find a necessary and sufficient condition for which a point star-configuration in Pn has generic Hilbert function. More precisely, a point star-configuration in Pn defined by general forms of degrees d1, . . . , ds with 3 ≤ n ≤ s has generic Hilbert function if and only if d1 = · · · = ds−1 = 1 and ds = 1, 2. Otherwise, the Hilbert function of a point star-configuration in Pn is NEVER generic.

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