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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We thank the referees for their careful and patient reading of the first version of our manuscript.
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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
Keywords
- Polynomial mapping
- Fibration
- Bifurcation points
- Malgrange’s Condition
- Nonproperness set of a polynomial mapping