Gorenstein Associated Graded Rings of Analytic Deviation Two Ideals

This paper studies the question of when the associated graded ring (I) n ≥ 0In/In + 1 of a certain ideal I in a local ring is Gorenstein. The main result implies, for example, that if A is a regular local ring, 708 is a prime ideal in A with dim A/ = 2, and A/ is a complete intersection in codimension one, then the associated graded ring ( ) is Gorenstein if and only if the reduction number of is at most 1.