On delta invariants and indices of ideals

2017/05/15 by Kobayashi, Toshinori · 1 citation
#13A30 #13C14 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.05042

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 invarints. 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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