The regularity index of seven almost equimultiple points in projective space \(\mathbb{P}^4\)

Abstract. In this paper, we compute the regularity index of the set of seven almost equimultiple points and give an example for the set of equimultiple points in projective space \(\mathbb{P}^3\) which does not attain Segre's upper bound.

Key words and phrases. Fat points, regularity index, zero-scheme.