[Non réalité et non connectivité des polynômes complexes]
Pour les polynômes de deux variables complexes, nous construisons des contre-exemples aux questions suivantes : à équivalence topologique près, peut-on toujours trouver une équation réelle à un polynôme complexe (Lee Rudolph) ? Deux polynômes topologiquement équivalents peuvent-ils être reliés par une famille de polynômes topologiquement équivalents ?
Using the same method we provide negative answers to the following questions: is it possible to find real equations for complex polynomials in two variables up to topological equivalence (Lee Rudolph)? Can two topologically equivalent polynomials be connected by a continuous family of topologically equivalent polynomials?
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@article{CRMATH_2002__335_12_1039_0,
author = {Bodin, Arnaud},
title = {Non-reality and non-connectivity of complex polynomials},
journal = {Comptes Rendus. Math\'ematique},
pages = {1039--1042},
publisher = {Elsevier},
volume = {335},
number = {12},
year = {2002},
doi = {10.1016/S1631-073X(02)02597-9},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02597-9/}
}
TY - JOUR AU - Bodin, Arnaud TI - Non-reality and non-connectivity of complex polynomials JO - Comptes Rendus. Mathématique PY - 2002 SP - 1039 EP - 1042 VL - 335 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02597-9/ DO - 10.1016/S1631-073X(02)02597-9 LA - en ID - CRMATH_2002__335_12_1039_0 ER -
%0 Journal Article %A Bodin, Arnaud %T Non-reality and non-connectivity of complex polynomials %J Comptes Rendus. Mathématique %D 2002 %P 1039-1042 %V 335 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02597-9/ %R 10.1016/S1631-073X(02)02597-9 %G en %F CRMATH_2002__335_12_1039_0
Bodin, Arnaud. Non-reality and non-connectivity of complex polynomials. Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 1039-1042. doi : 10.1016/S1631-073X(02)02597-9. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02597-9/
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