Journal of Commutative Algebra

Postulation and reduction vectors of multigraded filtrations of ideals

Parangama Sarkar and J.K. Verma

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We study the 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 generalization 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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J. Commut. Algebra, Volume 9, Number 4 (2017), 563-597.

First available in Project Euclid: 14 October 2017

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Primary: 13A02: Graded rings [See also 16W50] 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series 13D45: Local cohomology [See also 14B15]

Hilbert function joint reductions complete reductions Rees algebra Kirby-Mehran complex postulation and reduction vectors


Sarkar, Parangama; Verma, J.K. Postulation and reduction vectors of multigraded filtrations of ideals. J. Commut. Algebra 9 (2017), no. 4, 563--597. doi:10.1216/JCA-2017-9-4-563.

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