Complete algebraic vector fields on affine surfaces. I
The author studies holomorphic vector fields on an algebraic affine surface \(M\). Such a vector field is complete if it is `tangent' to a holomorphic flow \(M \times C \to M\). The singularities at infinity of the associated foliation are classified under mild assumptions. A sufficent condition is shown on these singularities that ensures the existence of the meromorphic first integral of the foliation. A special case of the result recovers a part of \textit{M. Brunella}'s [Topology 43, No.~2, 433--445 (2004; Zbl 1047.32015)] classification of complete polynomial vector fields on the complex plane.
scientific article; zbMATH DE number 2064457
scientific article