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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 R P 3 dont la courbe parabolique, lisse, a d ( d − 4 ) 2 composantes connexes.

On the number of connected components of the parabolic curve