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arXiv · 0901.3825

Filter-regular sequences and mixed multiplicities

Nguyen Tien Manh·Duong Quoc Viet
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Abstract

Let $S$ be a finitely generated standard multigraded algebra over an Artinian local ring $A$; $M$ a finitely generated multigraded $S$-module. This paper answers to the question when mixed multiplicities of $M$ are positive and characterizes them in terms of lengths of $A$-modules. As an application, we get results on mixed multiplicities of ideals (Proposition 4.4 and Theorem 4.5), and recover the results of Risler and Teissier [Te](see Remark 4.8), Trung and Verma [TV](see Remark 4.6).

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Nguyen Tien Manh, Duong Quoc Viet. 2009-01-24. Filter-regular sequences and mixed multiplicities. https://arxiv.org/abs/0901.3825

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