Summary
We prove that natural generating functions for enumeration of branched coverings of the pillowcase orbifold are level 2 quasimodular forms. This gives a way to compute the volumes of the strata of the moduli space of quadratic differentials.
To Vladimir Drinfeld on his 50th birthday.
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Eskin, A., Okounkov, A. (2006). Pillowcases and quasimodular forms. In: Ginzburg, V. (eds) Algebraic Geometry and Number Theory. Progress in Mathematics, vol 253. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4532-8_1
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DOI: https://doi.org/10.1007/978-0-8176-4532-8_1
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