[Sur le nombre de composantes connexes de la courbe parabolique]
À l'aide du patchwork de Viro, nous construisons un polyôme de degré d en deux variables dont la courbe Hessienne a composantes connexes. Cela implique en particulier l'existence d'une surface algébrique réelle de degré d dans dont la courbe parabolique, lisse, a composantes connexes.
We construct a polynomial of degree d in two variables whose Hessian curve has connected components using Viro patchworking. In particular, this implies the existence of a smooth real algebraic surface of degree d in whose parabolic curve is smooth and has connected components.
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@article{CRMATH_2010__348_5-6_287_0,
author = {Bertand, Beno{\^\i}t and Brugall\'e, Erwan},
title = {On the number of connected components of the parabolic curve},
journal = {Comptes Rendus. Math\'ematique},
pages = {287--289},
publisher = {Elsevier},
volume = {348},
number = {5-6},
year = {2010},
doi = {10.1016/j.crma.2010.01.028},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.01.028/}
}
TY - JOUR AU - Bertand, Benoît AU - Brugallé, Erwan TI - On the number of connected components of the parabolic curve JO - Comptes Rendus. Mathématique PY - 2010 SP - 287 EP - 289 VL - 348 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.01.028/ DO - 10.1016/j.crma.2010.01.028 LA - en ID - CRMATH_2010__348_5-6_287_0 ER -
%0 Journal Article %A Bertand, Benoît %A Brugallé, Erwan %T On the number of connected components of the parabolic curve %J Comptes Rendus. Mathématique %D 2010 %P 287-289 %V 348 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.01.028/ %R 10.1016/j.crma.2010.01.028 %G en %F CRMATH_2010__348_5-6_287_0
Bertand, Benoît; Brugallé, Erwan. On the number of connected components of the parabolic curve. Comptes Rendus. Mathématique, Tome 348 (2010) no. 5-6, pp. 287-289. doi : 10.1016/j.crma.2010.01.028. http://www.numdam.org/articles/10.1016/j.crma.2010.01.028/
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