Higher Iterated Hilbert Coefficients of the Graded Components of Bigraded Modules

Abstract

Let S = K[x1, …, xn] be the polynomial ring over a field K, and let I ⊂ S be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded S-modules [Formula: see text](M, Ik) and [Formula: see text](M, Ik) are polynomial functions in k, and an upper bound for their degree is given. These results are derived by considering suitable bigraded modules.