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.
Toshinori KOBAYASHI. "On delta invariants and indices of ideals." J. Math. Soc. Japan 71 (2) 589 - 597, April, 2019. https://doi.org/10.2969/jmsj/78297829