Abstract
We will give a formula to compute the regularity index of s + 2 fat points not lying on a linear (s − 1)-space in ℙ n , s ≤ n (Theorem 3.4). Our result generalizes a formula to compute the regularity index of fat points in general position in ℙ n ([3], Corollary 8). Our result also shows that the Segre bound is attained by s + 2 points not lying on a linear (s − 1)-space.
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