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arXiv · 1905.04524

Loop equations and a proof of Zvonkine's $qr$-ELSV formula

Petr Dunin-Barkowski·Reinier Kramer·Alexandr Popolitov·Sergey Shadrin
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Abstract

We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called $r$-ELSV formula, as well as its orbifold generalization, the $qr$-ELSV formula, proposed recently in [KLPS17].

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Petr Dunin-Barkowski, Reinier Kramer, Alexandr Popolitov, Sergey Shadrin. 2019-05-11. Loop equations and a proof of Zvonkine's $qr$-ELSV formula. https://doi.org/10.24033/asens.2553

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