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Singularités des flots holomorphes. II. (Singularities of holomorphic flows. II.). (French) Zbl 0938.32019
Ann. Inst. Fourier 47, No. 4, 1117-1174 (1997); erratum ibid. 50, No. 3, 1019-1020 (2000).
Summary: In part I [Ann. Inst. Fourier 46, No.2, 411-428 (1996; Zbl 0853.34002)], the second author showed, in particular, that a complete holomorphic vector field on a complex surface cannot have an isolated singularity with a vanishing second jet. In this paper, we give a precise description of complete holomorphic vector fields on complex surfaces admitting an isolated singularity with trivial first jet. If the ambient surface is compact, we describe explicitly all possible surfaces and vector fields.

32S65 Singularities of holomorphic vector fields and foliations
37F75 Dynamical aspects of holomorphic foliations and vector fields
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