Geometric aspects of Painlevé equations

@article{Kajiwara2015GeometricAO,
  title={Geometric aspects of Painlev{\'e} equations},
  author={Kenji Kajiwara and Masatoshi Noumi and Yasuhiko Yamada},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2015},
  volume={50}
}
In this paper a comprehensive review is given on the current status of achievements in the geometric aspects of the Painlevé equations, with a particular emphasis on the discrete Painlevé equations. The theory is controlled by the geometry of certain rational surfaces called the spaces of initial values, which are characterized by eight point configuration on P 1 × P 1 and classified according to the degeneration of points. We give a systematic description of the equations and their various… 

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