LEFSCHETZ PRINCIPLE APPLIED TO SYMBOLIC POWERS

In this paper, an alternative proof is presented of the following result on symbolic powers due to Ein, Lazarsfeld and Smith [3] (for the affine case over [Formula: see text]) and to Hochster and Huneke [4] (for the general case). Let A be a regular ring containing a field K. Let [Formula: see text] be a radical ideal of A and let h be the maximum of the heights of its minimal primes. Then for all n, we have an inclusion [Formula: see text], where the first ideal denotes the hnth symbolic power of [Formula: see text]. In prime characteristic, this result admits an easy tight closure proof due to Hochster and Huneke. In this paper, the characteristic zero version is obtained from this by an application of the Lefschetz Principle.