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Zeroes of complete polynomial vector fields |
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| Authors: | Alvaro Bustinduy |
| Institution: | Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense de Madrid, Ciudad Universitaria 28040 Madrid, Spain |
| Abstract: | We prove that a complete polynomial vector field on  has at most one zero, and analyze the possible cases of those with exactly one which is not of Poincaré-Dulac type. We also obtain the possible nonzero first jet singularities of the foliation  at infinity and the nongenericity of completeness. Connections with the Jacobian Conjecture are established. |
| Keywords: | Complete vector field complex orbit holomorphic foliation |
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