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Rigid meromorphic foliations on complex surfaces. (English) Zbl 0963.32020
The author first gives a construction of singular meromorphic foliations without algebraic leaves on every smooth projective surface. Then he gives a new proof of a result of L. G. Mendes and M. Sebastiani [Ann. Inst. Fourier 44, No. 1, 271-276 (1994; Zbl 0792.58001)]: On a smooth projective surface of Kodaira dimension \(-\infty\), except the complex projective plane, there is a rigid singular meromorphic foliation, which is induced by a ruling. Finally, rigidity is also studied for the case of an elliptic fibration.
MSC:
32S65 Singularities of holomorphic vector fields and foliations
58A17 Pfaffian systems
32S05 Local complex singularities
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