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arXiv · 1601.05622

Postulation and reduction vectors of multigraded filtrations of ideals

Parangama Sarkar·J. K. Verma
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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 $\mathcal F.$

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Parangama Sarkar, J. K. Verma. 2016-01-21. Postulation and reduction vectors of multigraded filtrations of ideals. https://arxiv.org/abs/1601.05622

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