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arXiv · 1403.5181

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

Kartoue Mady Demdah
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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.

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Kartoue Mady Demdah. 2016-05-13. Simultaneous resolution of singularities in the Nash category: finiteness and effectiveness. https://doi.org/10.1007/s13163-015-0176-8

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