Proper trajectories of type C* of a polynomial vector field on C2

Details Proper trajectories of type C* of a polynomial vector field on C2 Proper trajectories of type C* of a polynomial vector field on C2

2010-10-28

arxiv.org/abs/1010.6055v1

Mathematics

Complex Variables

To appear in Mathematische Annalen

Scientific paper

We prove that if a polynomial vector field on C2 has a proper and
non-algebraic trajectory analytically isomorphic to C* all its trajectories are
proper, and except at most one which is contained in an algebraic curve of type
C all of them are of type C*. As corollary we obtain an analytic version of
Lin-Zaidenberg Theorem for polynomial foliations.

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