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Communications in Mathematical Physics

, Volume 242, Issue 1–2, pp 185–219 | Cite as

An Area-Preserving Action of the Modular Group on Cubic Surfaces and the Painlevé VI Equation

  • Katsunori IwasakiEmail author
Article

Abstract

We construct an area-preserving action of the modular group on a general 4-parameter family of affine cubic surfaces. We present a geometrical background behind this construction, that is, a natural symplectic structure on a moduli space of rank two linear monodromy representations over the 2-dimensional sphere with four punctures, and a natural symplectic action upon it of the braid group on three strings. Studying this action as a discrete dynamical system will be important in discussing the monodromy of the Painlevé VI equation.

Keywords

Dynamical System Modulus Space Symplectic Structure Braid Group Modular Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Faculty of MathematicsKyushu UniversityHigashi-kuJapan

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