Open Access
April, 2019 On delta invariants and indices of ideals
J. Math. Soc. Japan 71(2): 589-597 (April, 2019). DOI: 10.2969/jmsj/78297829


Let $R$ be a Cohen–Macaulay local ring with a canonical module. We consider Auslander's (higher) delta invariants of powers of certain ideals of $R$. Firstly, we shall provide some conditions for an ideal to be a parameter ideal in terms of delta invariants. As an application of this result, we give upper bounds for orders of Ulrich ideals of $R$ when $R$ has Gorenstein punctured spectrum. Secondly, we extend the definition of indices to the ideal case, and generalize the result of Avramov–Buchweitz–Iyengar–Miller on the relationship between the index and regularity.


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Toshinori KOBAYASHI. "On delta invariants and indices of ideals." J. Math. Soc. Japan 71 (2) 589 - 597, April, 2019.


Received: 17 June 2017; Revised: 3 December 2017; Published: April, 2019
First available in Project Euclid: 25 February 2019

zbMATH: 07090057
MathSciNet: MR3943452
Digital Object Identifier: 10.2969/jmsj/78297829

Primary: 13A30 , 13C14 , 16G50

Keywords: Cohen–Macaulay approximation , delta invariant , Ulrich ideal

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 2 • April, 2019
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