Tropical Open Hurwitz numbers

Benoît Bertrand (1) , Erwan Brugalle (2) , Grigory Mikhalkin (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IMJ - Institut de Mathématiques de Jussieu
3 UNIGE - Université de Genève = University of Geneva

We give a tropical interpretation of Hurwitz numbers extending the one discovered in \cite{CJM}. In addition we treat a generalization of Hurwitz numbers for surfaces with boundary which we call open Hurwitz numbers.

Mots clés: Parabolic curve; Viro Method

Domaines: Géométrie algébrique [math.AG]; Topologie géométrique [math.GT]

Benoît Bertrand, Erwan Brugalle, Grigory Mikhalkin. Tropical Open Hurwitz numbers. Rendiconti del Seminario Matematico della Università di Padova, 2011, Volume 125, pp. 157-171. ⟨10.4171/RSMUP/125-10⟩. ⟨hal-00967490⟩