Open Access
October 2017 Semicomplete vector fields on non-Kähler surfaces
Adolfo Guillot
Proc. Japan Acad. Ser. A Math. Sci. 93(8): 73-76 (October 2017). DOI: 10.3792/pjaa.93.73


We investigate semicomplete meromorphic vector fields on complex surfaces, those where the solutions of the associated ordinary differential equations have no multivaluedness. We prove that if a non-Kähler compact complex surface has such a vector field, then, up to a bimeromorphic transformation, either the vector field is holomorphic, has a first integral or preserves a fibration. This extends previous results of Rebelo and the author to the non-Kähler setting.


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Adolfo Guillot. "Semicomplete vector fields on non-Kähler surfaces." Proc. Japan Acad. Ser. A Math. Sci. 93 (8) 73 - 76, October 2017.


Published: October 2017
First available in Project Euclid: 3 October 2017

zbMATH: 06836092
MathSciNet: MR3709270
Digital Object Identifier: 10.3792/pjaa.93.73

Primary: 34M45
Secondary: 32S65

Keywords: Enoki surface , Foliation , Semicompleteness

Rights: Copyright © 2017 The Japan Academy

Vol.93 • No. 8 • October 2017
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