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Polynomial and regular images of ℝn

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Abstract

We obtain new necessary conditions for ann-dimensional semialgebraic subset of ℝn to be a polynomial image of ℝn. Moreover, we prove that a large family of planar bidimensional semialgebraic sets with piecewise linear boundary are images of polynomial or regular maps, and we estimate in both cases the dimension of their generic fibers.

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Authors and Affiliations

  1. Depto. Matemáticas, Facultad de Ciencias, Univ. Autónoma de Madrid, 28049, Cantoblanco, Madrid, Spain

    José F. Fernando

  2. Depto. Álgebra, Facultad de Ciencias Matemáticas, Univ. Complutense de Madrid, 28040, Madrid, Spain

    J. M. Gamboa

Authors
  1. José F. Fernando
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  2. J. M. Gamboa
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Corresponding author

Correspondence to José F. Fernando.

Additional information

Supported by Spanish GAAR BFM2002-04797 and European RAAG HPRN-CT-2001-00271.

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Fernando, J.F., Gamboa, J.M. Polynomial and regular images of ℝn . Isr. J. Math. 153, 61–92 (2006). https://doi.org/10.1007/BF02771779

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  • DOI: https://doi.org/10.1007/BF02771779

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