On the number of connected components of the parabolic curve

Benoît Bertrand (1) , Erwan Brugallé (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IMJ - Institut de Mathématiques de Jussieu

We construct a polynomial of degree d in two variables whose Hessian curve has (d-2)^2 connected components using Viro patchworking. In particular, this implies the existence of a smooth real algebraic surface of degree d in RP^3 whose parabolic curve is smooth and has d(d-2)^2 connected components.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Benoît Bertrand, Erwan Brugallé. On the number of connected components of the parabolic curve. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2010. ⟨hal-02175241⟩