Fonction asymptotique de Samuel des sections hyperplanes et multiplicité

HICKEL, Michel

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HICKEL, Michel
Institut de Mathématiques de Bordeaux [IMB]

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Document de travail - Pré-publication

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Let $(A,\mathfrak{m}_A,k)$ be a local noetherian ring and $I$ an $\mathfrak{m}_A$-primary ideal. The asymptotic Samuel function (with respect to $I$) $\overline{v}_I$ $:$ $A\longrightarrow \mathbb{R}\cup {+\infty}$ is defined by $\overline{v}_I(x)=lim_{k \rightarrow \+infty}\frac{ord_I(x^k}{k}$, $\forall x \in A$. Similary, one defines for another ideal $J$, $\overline{v}_I(J)$ as the minimum of $\overline{v}_I(x)$ as $x$ varies in $J$. Of special interest is the rational number $\overline{v}_I(\mathfrak{m}_A)$. We study the behavior of the Asymptotic Samuel Function (with respect to $I$) when passing to hyperplanes sections of $A$ as one does for the theory of mixed multiplicities.< Leer menos

Palabras clave en inglés

Asymptotic Samuel function

Hyperplanes sections

Integral closure of ideals

Multiplicity

"Asymptotic Samuel function"

"Hyperplanes sections"

"Integral closure of ideals"

"Multiplicity"

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