Cubic Pencils and Painlev\'e HamiltoniansPreprint English OPEN
Kajiwara, Kenji; Masuda, Tetsu; Noumi, Masatoshi; Ohta, Yasuhiro; Yamada, Yasuhiko; (2004)
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.