Orbitwise countings in $\mathcal{H}(2)$ and quasimodular forms

Résumé

We prove formulae for the countings by orbit of square-tiled surfaces of genus two with one singularity. These formulae were conjectured by Hubert and Lelièvre. We show that these countings admit quasimodular forms as generating functions.

Type
Publication
Int. Math. Res. Not.