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arXiv · 1609.09008

Nash multiplicities and isolated points of maximum multiplicity

Beatriz Pascual-Escudero
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Abstract

Let $X$ be an algebraic variety defined over a field of characteristic zero, and let $\xi \in \mathrm{\underline{Max}\; mult}(X)$ be a point in the closed subset of maximum multiplicity of $X$. We provide a criterion, given in terms of arcs, to determine whether $\xi $ is isolated in $\mathrm{\underline{Max}\; mult}(X)$. More precisely, we use invariants of arcs derived from the Nash multiplicity sequence to characterize when $\xi $ is an isolated point in $\mathrm{\underline{Max}\; mult}(X)$.

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Beatriz Pascual-Escudero. 2016-09-28. Nash multiplicities and isolated points of maximum multiplicity. https://doi.org/10.1016/j.jpaa.2018.09.009

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