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

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.

Article de revue

International Mathematics Research Notices 2006, No. 11, Article ID 42151, 30 p