Analytic spread and non-vanishing of asymptotic depth

作者：Miranda Neto Cleto B^*

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2017, 163(2): 289-299.

DOI：10.1017/S0305004116001018

Let S be a polynomial ring over a field K of characteristic zero and let M subset of 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 subset of S containing M be such that the localisation M-P 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.

• 出版日期2017-9