Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
DOI:
https://doi.org/10.17268/sel.mat.2024.02.07Keywords:
Vector fields, Lie bracket, holomorphic action, singular setAbstract
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.
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