The regularity index of \(s\) fat points in projective
space \(\mathbb{P}^2\), \(s\le 6\)

Abstract. In this paper, we compute the regularity index of a set of five almost equimultiple (Theorem 3.2) and a set of six double points in general position in projective space \(\mathbb P^2\)
(Theorem 4.2).