Algebraic Geometry
On the number of connected components of the parabolic curve

Presented by: Christophe Soulé

Bertand, Benoît1; Brugallé, Erwan2
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
Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 287-289.

We construct a polynomial of degree d in two variables whose Hessian curve has (d−4)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(d−4)2 connected components.

À l'aide du patchwork de Viro, nous construisons un polyôme de degré d en deux variables dont la courbe Hessienne a (d−4)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(d−4)2 composantes connexes.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.01.028
Bertand, Benoît 1; Brugallé, Erwan 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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Bertand, Benoît; Brugallé, Erwan. 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://www.numdam.org/articles/10.1016/j.crma.2010.01.028/

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