Segre's upper bound for the regularity index of
\(2n+2\) non-degenerate double points in \(\Bbb P^n\)

Abstract. We prove the Segre's upper bound for the regularity index of \(2n+2\) non-degenerate double points that do not exist \(n+1\) points lying on a \((n-2)\)-plane in \(\Bbb P^n\).