Revista Matemática Complutense

, Volume 29, Issue 1, pp 207–224 | Cite as

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

  • Demdah Kartoue MadyEmail author


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.


Nash manifolds Resolution Singularities Real spectrum Blow-Nash 

Mathematics Subject Classification

14P10 14P20 



I would like to thank Michel Coste for his advice during the preparation of this paper. I also would like to thank the anonymous referees for reading carefully the previous version and for their remarkable suggestions.


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Copyright information

© Universidad Complutense de Madrid 2015

Authors and Affiliations

  1. 1.Département de Mathématiques, Faculté des Sciences Exactes et AppliquéesUniversité de NdjamenaN’DjamenaChad

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