,Higher Iterated Hilbert Coefficients of the Graded Components of Bigraded Modules

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Let S =K[x1,...,xn] be the polynomial ring over a field K,and let I (C) S be a graded ideal.It is shown that the higher iterated Hilbert coefficients of the graded S-modules TioriS(M,Ik) and ExtSi(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.
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