Abstract

Given two m -primary ideals a and I in a Noetherian local or graded ring, we introduce the level ideals of I with respect to a as a measure of the asymptotic growth of the drop in the joint Hilbert–Kunz multiplicity, e HK ( a t , I ) − e HK ( a t , ( I , x ) ) . We study the properties that must hold for two ideals a , b to determine the same level ideals for all I , and we show that this is related to projective equivalence.

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