Enumeration of Real Conics and Maximal Configurations

Erwan Brugallé (1) , Nicolas Puignau (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 UFRJ - Universidade Federal do Rio de Janeiro [Brasil] = Federal University of Rio de Janeiro [Brazil] = Université fédérale de Rio de Janeiro [Brésil]

We use floor decompositions of tropical curves to prove that any enumerative problem concerning conics passing through projective-linear subspaces in $\RP^n$ is maximal. That is, there exist generic configurations of real linear spaces such that all complex conics passing through these constraints are actually real.

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

Erwan Brugallé, Nicolas Puignau. Enumeration of Real Conics and Maximal Configurations. Journal of the European Mathematical Society, 2013, 15 (6), pp.2139-2164. ⟨10.4171/JEMS/418⟩. ⟨hal-02175153⟩