Fonction asymptotique de Samuel des sections hyperplanes et multiplicité
Langue
fr
Document de travail - Pré-publication
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
Mots clés en anglais
Asymptotic Samuel function
Hyperplanes sections
Integral closure of ideals
Multiplicity
"Asymptotic Samuel function"
"Hyperplanes sections"
"Integral closure of ideals"
"Multiplicity"
Origine
Importé de halUnités de recherche