  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
Mart\'{i}-Farr\'{e}.
