Loop equations and a proof of Zvonkine's $qr$-ELSV formula
Algebraic Geometry
2023-11-21 v4 Mathematical Physics
Combinatorics
math.MP
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 -ELSV formula, as well as its orbifold generalization, the -ELSV formula, proposed recently in [KLPS17].
Keywords
Cite
@article{arxiv.1905.04524,
title = {Loop equations and a proof of Zvonkine's $qr$-ELSV formula},
author = {Petr Dunin-Barkowski and Reinier Kramer and Alexandr Popolitov and Sergey Shadrin},
journal= {arXiv preprint arXiv:1905.04524},
year = {2023}
}
Comments
22 pages. Version 4: improved exposition of the proof