Painlevé VI equations with algebraic solutions and family of curves

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In families of Painlevé VI differential equations having common algebraic solutions we classify all the members which come from geometry, i.e. the corresponding linear differential equations which are Picard-Fuchs associated to families of algebraic varieties. In our case, we have one family with zero dimensional fibers and all others are families of curves. We use the classification of families of elliptic curves with four singular fibers done by Herfurtner in 1992 and generalize the results of Doran in 2001 and Ben Hamed and Gavrilov in 2005.
15 pages

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Algebraic Geometry, Classical Analysis and ODEs, 34M55

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http://salesiana.dossiersoluciones.com/handle/123456789/162436

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0806.1213
 http://arxiv.org/abs/0806.1213

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arXiv