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

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392635

Digital Object Identifier
doi:10.3792/pjaa.78.131

Mathematical Reviews number (MathSciNet)
MR1930217

Zentralblatt MATH identifier
1058.34125

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

Keywords
Modular group complex cubic surface nonlinear monodromy the Painlevé VI equation

Citation

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. https://projecteuclid.org/euclid.pja/1148392635


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