Séminaire de Géométrie Tropicale
13 février 2013, 16h15 salle 1525-502
Hannah Markwig
(Universität des Saarlandes)
Résumé :
Tropical Hurwitz cycles
Double Hurwitz numbers
count genus g degree d covers of the projective line with fixed
ramification profile over zero and infinity and only simple ramification
otherwise. They are piece-wise polynomial in the entries of the two
special ramification profiles. The wall-crossing formulas can be expressed
in terms of "smaller" Hurwitz numbers. Tropical analogues of double
Hurwitz numbers have been helpful to discover some of their interesing
features. We can also understand a double Hurwitz numbers as a
zero-dimensional cycle in an appropriate moduli space of covers, resp. Ist
push-forward into the moduli space of n-marked stable curves. We
generalize this point of view by allowing higher-dimensional cycles
corresponding to covers where we do not fix all simple ramification
points. We start by restricting to the case of genus zero. We consider
both the tropical and algebraic version of these generalized Hurwitz
cycles and study their connection, their piece-wise polynomial structure
and wall-crossing behavious. In this talk, we will concentrate on tropical
Hurwitz cycles.
This is a joint work with Aaron Bertram and Renzo Cavalieri.