3 0 Ju n 20 05 Families of Painlevé VI equations having a common solution
نویسنده
چکیده
We classify all functions satisfying non-trivial families of PVIα equations. It turns out that all of these 23 solutions are of geometric origin: they are related to deformations of elliptic surfaces as proved earlier by Doran. Similarly, we prove that the same solutions can be obtained from deformations of three-sheeted covers of P1 with branching locus consisting of four points. e-mail: [email protected] e-mail: [email protected]
منابع مشابه
Se p 20 05 Families of Painlevé VI equations having a common solution
We classify all functions satisfying non-trivial families of PVIα 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 P1 wit...
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