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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
Article

Abstract

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.

Keywords

Nash manifolds Resolution Singularities Real spectrum Blow-Nash 

Mathematics Subject Classification

14P10 14P20 

Notes

Acknowledgments

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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