Asymptotic behavior of grade of some modules via linkage

Abstract

Assume that [Formula: see text] is a standard graded algebra over the local ring [Formula: see text], [Formula: see text] is a homogeneous ideal of [Formula: see text], [Formula: see text] is a finitely generated graded [Formula: see text]-module and [Formula: see text] denotes the irrelevant ideal of [Formula: see text]. In this paper, among other things, we study the asymptotic behavior of the set [Formula: see text] as [Formula: see text], in the case where [Formula: see text] and [Formula: see text] are homogenously linked over [Formula: see text].