Filter-regular sequences and mixed multiplicities

Details Filter-regular sequences and mixed multiplicities Filter-regular sequences and mixed multiplicities

2009-01-24

arxiv.org/abs/0901.3825v1

Mathematics

Commutative Algebra

23 pages

Scientific paper

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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