2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70085Let $A$ 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 MartÃ-Farré.14 pagesCommutative Algebra13B22 (Primary); 14C17 (Secondary)On the irreducible components of the form ring and an application to intersection cyclestext