Open Hurwitz numbers and the mKP hierarchy

Open Hurwitz numbers and the mKP hierarchy Full article

Journal

Journal of Geometry and Physics
ISSN: 0393-0440

Output data

Year: 2026, Volume: 223, Article number : 105783, Pages count : 16 DOI: 10.1016/j.geomphys.2026.105783

Tags

Riemann surfaces with, boundary Hurwitz, numbers Integrable, systems Modified KP hierarchy

Authors

Buryak Alexandr ^1,2,3 , Tessler Ran J. ⁴ , Troshkin Mikhail ¹

Affiliations

1	Faculty of Mathematics, National Research University Higher School of Economics, Usacheva str. 6, Moscow, 119048, Russian Federation
2	Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, Moscow, 121205, Russian Federation
3	Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Koptyug av. 4, Novosibirsk, 630090, Russian Federation
4	Department of Mathematics, Weizmann Institute of Science, POB 26, Rehovot 7610001, Israel

Funding (1)

Министерство науки и высшего образования РФ

075-15-2025-348

We give a natural definition of open Hurwitz numbers, where the weight of each ramifified covering includes an integer parameter Ntaken to the power that is equal to the number of boundary components of a Riemann surface with boundary mapping to CP1. We prove that the resulting sequence of partition functions, depending on N∈Z, is a tau sequence of the mKP hierarchy, or in other words it is a sequence of tau-functions of the KP hierarchy where each tau-function is obtained from the previous one by a Darboux transformation. Our result is motivated by a previous observation of Alexandrov and the first two authors that the refined intersection numbers on the moduli spaces of Riemann surfaces with boundary give a tau-sequence of the mKP hierarchy. ©2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Buryak A. , Tessler R.J. , Troshkin M.
Open Hurwitz numbers and the mKP hierarchy
Journal of Geometry and Physics. 2026. V.223. 105783 :1-16. DOI: 10.1016/j.geomphys.2026.105783 WOS Scopus OpenAlex

Submitted:	Nov 14, 2025
Accepted:	Feb 1, 2026
Published online:	Feb 3, 2026

Web of science:	WOS:001685446500001
Scopus:	2-s2.0-105029101751
OpenAlex:	W7127394394

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