A criterion for intersection multiplicity one

Abstract

Let X and Y be any pure dimensional subschemes of Pnk over an algebraically closed field K and let I(X) and I(Y) be the largest homogeneous ideals in K[x0,…, xn] defining X and Y, respectively. By a pure dimensional subscheme X of Pnk we shall always mean a closed pure dimensional subscheme without imbedded components, i.e., all primes belonging to I(X) have the same dimension.