Regularity Index of S + 2 Fat Points not on a Linear (S − 1)-Space

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.

Key Words:

• Fat point
• Regularity index
• Zero-scheme

2010 Mathematics Subject Classification:

• Primary 14C20
• Secondary 13D40

ACKNOWLEDGMENTS

The author gratefully acknowledges the many helpful suggestions of the referee.

Notes

Communicated by A. Singh.