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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Construction of invariant curves
for singular holomorphic vector fields

Author: J. Cano
Journal: Proc. Amer. Math. Soc. 125 (1997), 2649-2650
MSC (1991): Primary 34A05; Secondary 32S65
MathSciNet review: 1389507
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Abstract: Camacho and Sad proved the existence of invariant analytic curves for germs of singular holomorphic foliations ${{\cal F}}$ over a two dimensional complex analytic variety $M$. Their proof is only of existential nature. Here we provide a simple constructive proof by giving criteria to choose a singular point at each blowing-up that follows an analytic invariant curve.

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J. Cano
Affiliation: Facultad de Ciencias, Universidad de Valladolid, 47005-Valladolid, Spain

Received by editor(s): October 24, 1995
Received by editor(s) in revised form: March 19, 1996
Additional Notes: This work was supported by the I.A.S. under NSF grant # DMS-9304580.
Communicated by: Mary Rees
Article copyright: © Copyright 1997 American Mathematical Society