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Deformations of Frobenius structures on Hurwitz spaces

Vasilisa Shramchenko
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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.

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Vasilisa Shramchenko. 2004-11-12. Deformations of Frobenius structures on Hurwitz spaces. https://arxiv.org/abs/math-ph/0408026

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