Comptes Rendus
Algebraic Geometry
On the number of connected components of the parabolic curve
[Sur le nombre de composantes connexes de la courbe parabolique]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 287-289.

À l'aide du patchwork de Viro, nous construisons un polyôme de degré d en deux variables dont la courbe Hessienne a (d4)2 composantes connexes. Cela implique en particulier l'existence d'une surface algébrique réelle de degré d dans RP3 dont la courbe parabolique, lisse, a d(d4)2 composantes connexes.

We construct a polynomial of degree d in two variables whose Hessian curve has (d4)2 connected components using Viro patchworking. In particular, this implies the existence of a smooth real algebraic surface of degree d in RP3 whose parabolic curve is smooth and has d(d4)2 connected components.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.01.028

Benoît Bertand 1 ; Erwan Brugallé 2

1 Institut mathématique de Toulouse, I.U.T. de Tarbes, 1 rue Lautréamont, BP 1624, 65016 Tarbes, France
2 Université Pierre et Marie Curie, Institut Mathématiques de Jussieu, 175 rue du Chevaleret, 75 013 Paris, France
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Benoît Bertand; Erwan Brugallé. On the number of connected components of the parabolic curve. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 287-289. doi : 10.1016/j.crma.2010.01.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.01.028/

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