Deformations of Frobenius structures on Hurwitz spaces

Details Deformations of Frobenius structures on Hurwitz spaces Deformations of Frobenius structures on Hurwitz spaces

2004-08-15

arxiv.org/abs/math-ph/0408026v2

Int. Math. Res. Not. 2005, no.6, 339-387 (2005)

Physics

Mathematical Physics

36 pages, minor corrections

Scientific paper

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 Painlev\'e-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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