Deformations of Frobenius structures on Hurwitz spaces

Abstract

Deformations of Dubrovin's Hurwitz Frobenius manifolds are constructed. The deformations depend on $g(g+1)/2$ complex parameters where $g$ is the genus of the corresponding Riemann surface. In genus one, the flat metric of the deformed Frobenius manifold coincides with a metric associated with a one-parameter family of solutions to the Painlevé-VI equation with coefficients $(1/8,-1/8,1/8,3/8).$ Analogous deformations of the real doubles of the Hurwitz Frobenius manifolds are also found; these deformations depend on $g(g+1)/2$ real parameters.

36 pages, minor corrections

References in corpus (1)

• "Real doubles" of Hurwitz Frobenius manifolds

Cited by in corpus (1)

• A remark on deformations of Hurwitz Frobenius manifolds