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- Title
Analytic spread and non-vanishing of asymptotic depth.
- Authors
MIRANDA–NETO, CLETO B.
- Abstract
Let S be a polynomial ring over a field K of characteristic zero and let M ⊂ S be an ideal given as an intersection of powers of incomparable monomial prime ideals (e.g., the case where M is a squarefree monomial ideal). In this paper we provide a very effective, sufficient condition for a monomial prime ideal P ⊂ S containing M be such that the localisation MP has non-maximal analytic spread. Our technique describes, in fact, a concrete obstruction for P to be an asymptotic prime divisor of M with respect to the integral closure filtration, allowing us to employ a theorem of McAdam as a bridge to analytic spread. As an application, we derive – with the aid of results of Brodmann and Eisenbud-Huneke – a situation where the asymptotic and conormal asymptotic depths cannot vanish locally at such primes.
- Subjects
ASYMPTOTIC theory of system theory; POLYNOMIAL rings; PRIME ideals; MAXIMAL ideals; NOETHERIAN rings; MAXIMAL functions
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2017, Vol 163, Issue 2, p289
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004116001018