We prove the quasimodularity of generating functions for counting torus covers, with and without Siegel-Veech weight. Our proof is based on analyzing decompositions of flat surfaces into horizontal cylinders. The quasimodularity arise as contour integral of quasi-elliptic functions. It provides an alternative proof of …
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6 results for “quasimodularity”
Proves quasimodularity of generating functions for pillowcase covers.
problem Counting Feynman-like graphs associated with quadratic differentials.
method Analyzing decompositions of half-translation surfaces into horizontal cylinders.
result Alternative proof of quasimodularity results and practical method to compute area Siegel-Veech constants.
Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich on the large genus limits of Masur-Veech volumes and of Siegel-Veec…
We prove formulae for the countings by orbit of square-tiled surfaces of genus two with one singularity. These formulae were conjectured by Hubert & Lelièvre. We show that these countings admit quasimodular forms as generating functions.
Study refines Siegel-Veech constants for abelian differentials.
problem Computing Siegel-Veech constants for abelian differentials.
method Intersection theory and quasimodular forms.
result New identity for Siegel-Veech constants of cylinders.
Develops tropical geometry for weighted Hurwitz numbers, generalizing previous results.
problem Understanding weighted Hurwitz numbers across various cases.
method Tropical geometry framework for weighted Hurwitz numbers.
result Generalized structural results for weighted Hurwitz numbers.