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Reaching generalized critical values of a polynomial

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Abstract

Let \(f: \mathbb K ^n \rightarrow \mathbb K \) be a polynomial, \(\mathbb K =\mathbb R , \,\mathbb C \). We give an algorithm to compute the set of generalized critical values. The algorithm uses a finite dimensional space of rational arcs along which we can reach all generalized critical values of \(f\).

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Acknowledgments

We thank the referees for their careful and patient reading of the first version of our manuscript.

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Authors and Affiliations

  1. Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, 00-956 , Warszawa, Poland

    Zbigniew Jelonek

  2. LAMA Laboratoire de Mathématiques, UMR 5127 Université de Savoie, Campus scientifique, 73376 , Le Bourget du Lac Cedex, France

    Krzysztof Kurdyka

Authors
  1. Zbigniew Jelonek
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  2. Krzysztof Kurdyka
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Corresponding author

Correspondence to Krzysztof Kurdyka.

Additional information

Z. Jelonek was partially supported by Université de Savoie and by NCN(Poland), 2014–2017. K. Kurdyka was partially supported by ANR(France) grant STAAVF.

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Jelonek, Z., Kurdyka, K. Reaching generalized critical values of a polynomial. Math. Z. 276, 557–570 (2014). https://doi.org/10.1007/s00209-013-1213-2

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  • DOI: https://doi.org/10.1007/s00209-013-1213-2

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