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Nash multiplicities and isolated points of maximum multiplicity

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2019-06
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Elsevier
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Let X be an algebraic variety defined over a field of characteristic zero, and let ξ ∈ 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 ξ is isolated in Max mult(X). More precisely, we use invariants of arcs derived from the Nash multiplicity sequence to characterize when ξ is an isolated point in Max mult(X).
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Arc spaces, Resolution of singularities, Rees algebras
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Pascual-Escudero, B. (2019). Nash multiplicities and isolated points of maximum multiplicity. Journal of Pure and Applied Algebra, 223(6), 2598–2614.