Nash multiplicities and isolated points of maximum multiplicity

Abstract

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

minor corrections, 15 pages

References in corpus (2)

• Rees algebras and resolution of singularities
• Nash multiplicities and resolution invariants

Cited by in corpus (1)

• Contact loci and Hironaka's order