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2017 Postulation and reduction vectors of multigraded filtrations of ideals
Parangama Sarkar, J.K. Verma
J. Commut. Algebra 9(4): 563-597 (2017). DOI: 10.1216/JCA-2017-9-4-563


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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Parangama Sarkar. J.K. Verma. "Postulation and reduction vectors of multigraded filtrations of ideals." J. Commut. Algebra 9 (4) 563 - 597, 2017.


Published: 2017
First available in Project Euclid: 14 October 2017

zbMATH: 06797099
MathSciNet: MR3713528
Digital Object Identifier: 10.1216/JCA-2017-9-4-563

Primary: 13A02 , 13A30 , 13D40 , 13D45

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

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium


Vol.9 • No. 4 • 2017
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