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.
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.
Accepted:
Published online:
Benoît Bertand 1; Erwan Brugallé 2
@article{CRMATH_2010__348_5-6_287_0, author = {Beno{\^\i}t Bertand and Erwan Brugall\'e}, 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}, }
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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