Nash multiplicities and resolution invariants

  1. A. Bravo
  2. S. Encinas
  3. Beatriz Pascual Escudero
Aldizkaria:
Collectanea mathematica

ISSN: 0010-0757

Argitalpen urtea: 2017

Alea: 68

Faszikulua: 2

Orrialdeak: 175-217

Mota: Artikulua

DOI: 10.1007/S13348-016-0188-9 DIALNET GOOGLE SCHOLAR lock_openSarbide irekia editor

Beste argitalpen batzuk: Collectanea mathematica

Laburpena

The Nash multiplicity sequence was defined by Lejeune-Jalabert as a non-increasing sequence of integers attached to a germ of a curve inside a germ of a hypersurface. Hickel generalized this notion and described a sequence of blow ups which allows us to compute it and study its behavior. In this paper, we show how this sequence can be used to compute some invariants that appear in algorithmic resolution of singularities. Moreover, this indicates that these invariants from constructive resolution are intrinsic to the variety since they can be read in terms of its space of arcs. This result is a first step connecting explicitly arc spaces and algorithmic resolution of singularities.

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