Higher iterated Hilbert coefficients of the graded components of bigraded modules

2016/10/09 by Arkian, Seyed Shahab
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.02655

Abstract

Let S=K[x₁,…,x_n] be the polynomial ring over the field K, and let I⊂ S be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded S-modules \Tor_i^S(M,I^k) and \Extⁱ_S(M,I^k) 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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