Let (A, m) be a complete intersection of dimension d 1 and codimension c 1. Let I be an m-primary ideal and let M be a finitely generated A-module. For i 1 let ᵢI (M) be the degree of the polynomial type function n (ExtⁱA (M, A/Iⁿ) ). We show that for j = 0, 1 and for all i 0 we have ₂₈ +₉I (M) is a constant and let r₀I (M) and r₁I (M) denote these constant values. Set rI (M) = \ r₀I (M), r₁I (M) \. We show that rI (M) is an invariant of I, A and the support variety of M. We set the degree of the zero polynomial to be -. If rI (M) 0 then we show that reg \ GI (ⁱ (M) ) for i 0 is bounded. We give an application of this result to syzgetic Artin-Rees property of M. We also give several examples which illustrate our results.
Tony J. Puthenpurakal (Sun,) studied this question.