Asymptotic behaviour of graded local cohomology modules via linkage

Abstract

Assume that R = ⊕ n∈N0 R n is a standard graded algebra over the local ring (R 0 , m 0 ), a is a homogeneous ideal of R, M is a finitely generated graded R-module and R + := ⊕ n∈N R n denotes the irrelevant ideal of R. In this paper, we study the asymptotic behaviour of the set {grade(a ∩ R 0 , H grade(R+,M) R+ (M ) n )} n∈Z as n → −∞, in the case where a and R + are homogenously linked over M .