Proceedings of the Japan Academy, Series A, Mathematical Sciences

A modular group action on cubic surfaces and the monodromy of the Painlevé VI equation

Katsunori Iwasaki

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We construct an action of the modular group $\varGamma(2)$ on a general $4$-parameter family of complex cubic surfaces and describe the nonlinear monodromy of the Painlevé VI equation in terms of this action.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 7 (2002), 131-135.

First available in Project Euclid: 23 May 2006

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Zentralblatt MATH identifier

Primary: 33E17: Painlevé-type functions
Secondary: 14R20: Group actions on affine varieties [See also 13A50, 14L30]

Modular group complex cubic surface nonlinear monodromy the Painlevé VI equation


Iwasaki, Katsunori. A modular group action on cubic surfaces and the monodromy of the Painlevé VI equation. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 7, 131--135. doi:10.3792/pjaa.78.131.

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