Deformations of Frobenius structures on Hurwitz spaces
نویسنده
چکیده
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 real doubles of the Hurwitz Frobenius manifolds are also found; these deformations depend on g(g + 1)/2 real parameters.
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