Experimental Mathematics

Painlevé VI Equations with Algebraic Solutions and Family of Curves

Hossein Movasati and Stefan Reiter

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In families of Painlevé VI differential equations having common algebraic solutions we classify all the members that come from geometry, i.e., the corresponding linear differential equations that 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 carried out by Herfurtner in 1991 and generalize the results of Doran in 2001 and Ben Hamed and Gavrilov in 2005.

Article information

Experiment. Math., Volume 19, Issue 2 (2010), 161-173.

First available in Project Euclid: 17 June 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34M55: Painlevé and other special equations; classification, hierarchies; 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Painlevé sixth equation Okamoto transformation monodromy convolution


Movasati, Hossein; Reiter, Stefan. Painlevé VI Equations with Algebraic Solutions and Family of Curves. Experiment. Math. 19 (2010), no. 2, 161--173. https://projecteuclid.org/euclid.em/1276784787

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