Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials
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en
Article de revue
Ce document a été publié dans
Algebraic and Geometric Topology. 2020, vol. 20, n° 5, p. 2451-2510
Mathematical Sciences Publishers
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
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