Postulation and reduction vectors of multigraded filtrations of ideals

Abstract

We study relationship between postulation and reduction vectors of admissible multigraded filtrations $\mathcal{F}=\{\mathcal{F}(\underline{n}){\}}_{\underline{n}\in {\mathbb{Z}}^s}$ 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 $\mathcal{F}.$

arXiv comment25 pages