Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials

Elise Goujard; Martin Moeller

doi:10.2140/agt.2020.20.2451

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arXiv · 1809.05016

Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials

Elise Goujard·Martin Moeller

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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.

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BibTeX RIS

Elise Goujard, Martin Moeller. 2018-09-13. Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials. https://doi.org/10.2140/agt.2020.20.2451

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