Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simultaneous resolution of singularities in the Nash category:
  finiteness and effectiveness   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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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: econ