Gorenstein Associated Graded Rings of Analytic Deviation Two Ideals

AbstractThis paper studies the question of when the associated graded ring G(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/p=2, and A/p is a complete intersection in codimension one, then the associated graded ring G(p) is Gorenstein if and only if the reduction number of p is at most 1