Inflection Points of Real and Tropical Plane Curves

Erwan Brugallé (1) , Lucía López de Medrano (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 UNAM - Instituto de Matematicas

We prove that Viro's patchworking produces real algebraic curves with the maximal number of real inflection points. In particular this implies that maximally inflected real algebraic $M$-curves realize many isotopy types. The strategy we adopt in this paper is tropical: we study tropical limits of inflection points of classical plane algebraic curves. The main tropical tool we use to understand these tropical inflection points are tropical modifications.

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

Erwan Brugallé, Lucía López de Medrano. Inflection Points of Real and Tropical Plane Curves. Journal of Singularities, 2012, 4, pp.74-103. ⟨hal-02175140⟩