Families of Painleve VI equations having a common solution

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We classify all functions satisfying non-trivial families of PVI equations. It turns out that, up to an Okamoto equivalence, there are exactly four families parameterized by affine planes or lines. Each affine space is generated by points of "geometric origin", associated either to deformations of elliptic surfaces with four singular fibers, or to deformations of three-sheeted covers of the projective line with branching locus consisting of four points.
25 pages, 5 tables and 2 figures. The overall presentation is improved, the solution 1A is added to the main theorem, 3 figures and one table are removed (to save space)

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Classical Analysis and ODEs, Algebraic Geometry, 34M55

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http://salesiana.dossiersoluciones.com/handle/123456789/161919

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0507002
 http://arxiv.org/abs/math/0507002
 IMRN, 2005, No 60, pp. 3727-3752

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arXiv