On the Irreducible Components of the Form Ring and an Application to Intersection Cycles

Abstract

Let A be a commutative Noetherian ring and I an ideal in A. We characterize algebraically when all the minimal primes of the associated graded ring G I A contract to minimal primes of A/I. This, applied to intersection theory, means that there are no embedded distinguished varieties of intersection. The characterization is in terms of the analytic spread of certain localizations of I, the symbolic Rees algebra, and the normalization of the Rees algebra, and extends results of Huneke, Vasconcelos, and Martí-Farré.