MR2976043 Adolfo GUILLOT Adolfo GUILLOT The Geometry of Chazy's Homogeneous Third-Order Differential Equations Funkcialaj Ekvacioj. Serio Internacia 55 2012 67--87 http://fe.math.kobe-u.ac.jp/FE/FullPapers/55-1/55_67.pdf http://www.ams.org/mathscinet-getitem?mr=MR2976043 Chazy studied a family of homogeneous third-order autonomous differential equations. They are those, within a certain class, admitting exclusively single-valued solutions. Each one of these equations yields a polynomial vector field in complex three-dimensional space. For almost all of these these vector fields, the Zariski closure of a generic orbit yields an affine surface endowed with a holomorphic vector field that has exclusively single-valued solutions. We classify these surfaces and relate this classification to recent results of Rebelo and the author. Chazy equations, Painlevé property, Holomorphic vector field, Semicompleteness. 34M55, 34M45, 32M25. 55-67 2012 The Geometry of Chazy's Homogeneous Third-Order Differential Equations Adolfo GUILLOT Adolfo GUILLOT 1 Brunella, M. Birational geometry of foliations Monografías de Matemática, Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro 2000 MR1948251
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