Frobenius structures on double Hurwitz spaces

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

paper · doi:10.48550/arxiv.1210.2312

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

Related

• Genus zero Whitham hierarchy via Hurwitz--Frobenius manifolds
• New formula for the prepotentials associated with Hurwitz-Frobenius manifolds and generalized WDVV equations
• Finite Group Reduction of the DR/DZ Hierarchies
• Primitive forms and Frobenius structures on the Hurwitz spaces
• Generalized Frobenius Manifolds with Non-flat Unity and Integrable Hierarchies