Experimental Mathematics

Painlevé VI Equations with Algebraic Solutions and Family of Curves

Hossein Movasati and Stefan Reiter

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Abstract

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

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

Dates
First available in Project Euclid: 17 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.em/1276784787

Mathematical Reviews number (MathSciNet)
MR2676745

Zentralblatt MATH identifier
1215.34114

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

Keywords
Painlevé sixth equation Okamoto transformation monodromy convolution

Citation

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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