Nash multiplicities and resolution invariants Articles uri icon

publication date

  • May 2017

start page

  • 175

end page

  • 217


  • 2


  • 68

International Standard Serial Number (ISSN)

  • 0010-0757


  • 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.


  • Mathematics


  • rees algebras; resolution of singularities; arc spaces