Postulation and reduction vectors of multigraded filtrations of ideals

2016/01/21 by Sarkar, Parangama, Verma, J. K.
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.05622

Abstract

We study relationship between postulation and reduction vectors of admissible multigraded filtrations \mathcal F= \\mathcal F (\underline n)\_{\underline n∈\mathbb Z^s} of ideals in Cohen-Macaulay local rings of dimension at most two. This is enabled by a suitable generalisation of the Kirby-Mehran Complex. An analysis of its homology leads to an analogue of Huneke's Fundamental Lemma which plays a crucial role in our investigations. We also clarify the relationship between the Cohen-Macaulay property of the multigraded Rees algebra of \mathcal F and reduction vectors with respect to complete reductions of \mathcal F.

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