On the irreducible components of the form ring and an application to intersection cycles

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 $A\mathrm{/}I$. 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 Mart'{i}-Farr'{e}.