Fonction asymptotique de Samuel des sections hyperplanes et multiplicité
Language
fr
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Asymptotic Samuel function
Hyperplanes sections
Integral closure of ideals
Multiplicity
"Asymptotic Samuel function"
"Hyperplanes sections"
"Integral closure of ideals"
"Multiplicity"
Origin
Hal imported