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

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

2004-02-06

arxiv.org/abs/math/0402106v1

Mathematics

Commutative Algebra

14 pages

Scientific paper

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}.

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