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arXiv · 1805.01440

Mixed Multiplicities of Filtrations

Steven Dale Cutkosky·Parangama Sarkar·Hema Srinivasan
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Abstract

In this paper we define and explore properties of mixed multiplicities of (not necessarily Noetherian) filtrations of $m_R$-primary ideals in a Noetherian local ring $R$, generalizing the classical theory for $m_R$-primary ideals. We construct a real polynomial whose coefficients give the mixed multiplicities. This polynomial exists if and only if the dimension of the nilradical of the completion of $R$ is less than the dimension of $R$, which holds for instance if $R$ is excellent and reduced. We show that many of the classical theorems for mixed multiplicities of $m_R$-primary ideals hold for filtrations, including the famous Minkowski inequalities of Teissier, and Rees and Sharp.

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Steven Dale Cutkosky, Parangama Sarkar, Hema Srinivasan. 2018-05-03. Mixed Multiplicities of Filtrations. https://arxiv.org/abs/1805.01440

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