Collectanea Mathematica, Volume: 61 Number: 1

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Multiplicities and Rees valuations

Daniel Katz, Javid Validashti


Let $(R,\m)$ be a local ring of Krull dimension~$d$ and $I\subseteq R$ be an ideal with analytic spread~$d$. We show that the $j$-multiplicity of~$I$ is determined by the Rees valuations of~$I$ centered on~$\m$. We also discuss a multiplicity that is the limsup of a sequence of lengths that grow at an~$O(n^d)$ rate.

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