Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold - Benito Leonardo Ostos Cordero (Selecciones Matemáticas)
In this work, we study actions of the Lie group SL(2,C) on a complex manifold of dimension three or higher. It is demonstrated that these types of actions induce three complete holomorphic vector fields, one of which is periodic, and that there exists a particular relationship between them, given by the Lie bracket, which generates a singular holomorphic foliation of codimension two. Subsequently, the types of singularities are classified, and the normal forms of these vector fields are obtained in a neighborhood of each singular point of the foliation.