Communications in Number Theory and Physics

Volume 9 (2015)

Number 2

Dubrovin-Zhang hierarchy for the Hodge integrals

Pages: 239 – 271



A. Buryak (Department of Mathematics, ETH Zurich, Switzerland; and Department of Mathematics, Moscow State University, Moscow, Russia)


In this paper we prove that the generating series of the Hodge integrals over the moduli space of stable curves is a solution of a certain deformation of the KdV hierarchy. This hierarchy is constructed in the framework of the Dubrovin–Zhang theory of the hierarchies of the topological type. It occurs that our deformation of the KdV hierarchy is closely related to the hierarchy of the Intermediate Long Wave equation.

2010 Mathematics Subject Classification

14H10, 37K05

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Published 12 June 2015