On delta invariants and indices of ideals

Abstract

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.