Nash multiplicities and resolution invariants

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

ISSN: 0010-0757

Datum der Publikation: 2017

Ausgabe: 68

Faszikel: 2

Seiten: 175-217

Art: Artikel

DOI: 10.1007/S13348-016-0188-9 DIALNET GOOGLE SCHOLAR lock_openOpen Access editor

Andere Publikationen in: Collectanea mathematica

Zusammenfassung

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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