Simultaneous resolution of singularities in the Nash category: finiteness and effectiveness

Kartoue Mady Demdah (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we present new proofs using real spectra of the finiteness theorem on Nash trivial simultaneous resolution and the finiteness theorem on Blow-Nash triviality for isolated real algebraic singularities. That is, we prove that a family of Nash sets in a Nash manifold indexed by a semialgebraic set always admits a Nash trivial simultaneous resolution after a partition of the parameter space into finitely many semialgebraic pieces and in the case of isolated singularities it admits a finite Blow-Nash trivialization. We also complement the finiteness results with recursive bounds.

Mots clés: Blow-Nash; Nash manifolds; Resolution; Singularities; Real spectrum; Blow-Nash.

Domaines: Géométrie algébrique [math.AG]

Kartoue Mady Demdah. Simultaneous resolution of singularities in the Nash category: finiteness and effectiveness. 2015. ⟨hal-00962155v2⟩