Frobenius structures on double Hurwitz spaces

2012/10/08 by Stefano Romano, Romano, Stefano · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AG #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.1210.2312

28 pages

arxiv created 2012/10/08 · arxiv updated 2012/10/09

Abstract

We construct Frobenius structures of "dual type" on the moduli space of ramified coverings of ℙ¹ with given ramification type over two points, generalizing a construction of Dubrovin. A complete hierarchy of hydrodynamic type is obtained from the corresponding deformed flat connection. This provides a suitable framework for the Whitham theory of an enlarged class of integrable hierarchies; we treat as examples the q-deformed Gelfand-Dickey hierarchy and the sine-Gordon equation, and compute the corresponding solutions of the WDVV equations.

Cited by

• Dubrovin duality for open Hurwitz flat F-manifolds
• Bihamiltonian structure of the (n,1)-type rational reductions of the 2D-Toda hierarchy

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