Cubic Pencils and Painlev\'e Hamiltonians

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Kajiwara, Kenji; Masuda, Tetsu; Noumi, Masatoshi; Ohta, Yasuhiro; Yamada, Yasuhiko;
  • Subject: Nonlinear Sciences - Exactly Solvable and Integrable Systems | High Energy Physics - Theory | Mathematics - Algebraic Geometry
    arxiv: Mathematics::Algebraic Geometry | Mathematics::Symplectic Geometry

We present a simple heuristic method to derive the Painlev\'e differential equations from the corresponding geometry of rational surafces. We also give a direct relationship between the cubic pencils and Seiberg-Witten curves.
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