ar X iv : a lg - g eo m / 9 50 90 03 v 1 1 S ep 1 99 5 Generators for Symbolic Powers of Ideals

L et I be an ideal, homogeneous with respect to the usual grading, in a polynomial ring R = k[x0, . . . , xn] in n+ 1 variables (over an algebraically closed field k). Denote the graded component of I of degree d by Id, and likewise the k-vector space of homogeneous forms of R of degree d by Rd. Since I is a graded R-module, we have k-linear maps μd,i : Id ⊗ Ri → Id+i given for each i and d by multiplication; when the index i (or the indices i and d) are clear from context, we will denote μd,i by μd or simply μ.