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

IF 1.3 1区数学 Q1 MATHEMATICS Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-03 DOI:10.24033/asens.2553

Petr Dunin-Barkowski, Reinier Kramer, Alexandr Popolitov, Sergey Shadrin

引用次数: 16

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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循环方程和Zvonkine的$qr$-ELSV公式的证明

我们通过所谓的$r$-ELSV公式，以及最近在[KLPS17]中提出的$qr$-ELSV公式，证明了2006 Zvonkine猜想，该猜想用Chiodo类的交数表示具有完全循环的Hurwitz数。

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来源期刊

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.

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