The regularity index of 0-scheme of six almost equimultiple points in projective space P3 Trần Nam

Abstract

The denote by Pⁿ the projective space with its dimension is n,  is polynomial ring in variables  over the algebraic closed field. If A_i in Pⁿ and a_i in positive integer number. Let J be the power intersection of prime ideals generated by n linearly independent linear forms. The R/J ring is a positive-degree ring, the degree parts of which are k-vector spaces. The denote by G=a₁A₁+ +a_tA_t is 0-scheme defined by J. The regularity index of R/J (or G), denote by reg(R/J) (or reg(G)) is defined by the dimension of these k-vector spaces. However, computing reg(G) for an arbitrary set of points is not easy and there are very few results that can compute it. The author's result is to compute reg(G) for a set of six nearly equimultiple points given at any position in P³.