Translator Disclaimer
2020 Pillowcase covers: counting Feynman-like graphs associated with quadratic differentials
Elise Goujard, Martin Möller
Algebr. Geom. Topol. 20(5): 2451-2510 (2020). DOI: 10.2140/agt.2020.20.2451

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 and Okounkov and a practical method to compute area Siegel–Veech constants.

A main new technical tool is a quasipolynomiality result for 2 –orbifold Hurwitz numbers with completed cycles.

Citation

Download Citation

Elise Goujard. Martin Möller. "Pillowcase covers: counting Feynman-like graphs associated with quadratic differentials." Algebr. Geom. Topol. 20 (5) 2451 - 2510, 2020. https://doi.org/10.2140/agt.2020.20.2451

Information

Received: 17 October 2018; Revised: 29 August 2019; Accepted: 7 January 2020; Published: 2020
First available in Project Euclid: 10 November 2020

MathSciNet: MR4171571
Digital Object Identifier: 10.2140/agt.2020.20.2451

Subjects:
Primary: 11F11, 32G15
Secondary: 14H30, 14N10, 30F30, 81T18

Rights: Copyright © 2020 Mathematical Sciences Publishers

JOURNAL ARTICLE
60 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.20 • No. 5 • 2020
MSP
Back to Top