Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials
Geometric Topology
2020-11-11 v1 Algebraic Geometry
Number Theory
Abstract
We prove the quasimodularity of generating functions for counting pillowcase covers, with and without Siegel-Veech weight. Similar to prior work on torus covers, the proof is based on analyzing decompositions of half-translation surfaces into horizontal cylinders. It provides an alternative proof of the quasimodularity results of Eskin-Okounkov and a practical method to compute area Siegel-Veech constants. A main new technical tool is a quasi-polynomiality result for 2-orbifold Hurwitz numbers with completed cycles.
Cite
@article{arxiv.1809.05016,
title = {Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials},
author = {Elise Goujard and Martin Moeller},
journal= {arXiv preprint arXiv:1809.05016},
year = {2020}
}
Comments
Preliminary version, comments welcome!