Calvo-Andrade, Omegar Deformations of branched Lefschetz pencils. (English) Zbl 0843.58001 Bol. Soc. Bras. Mat., Nova Sér. 26, No. 1, 67-83 (1995). It is shown that in every projective manifold \(M\) of dimension \(>3\) and \(H^1 (M, C)= 0\) any deformation of a codimension one singular foliation \({\mathcal F}\) arising from the fibers of a generic meromorphic map of the form \(f^p/ g^q\), \(p,q>0\) has a meromorphic first integral of the same type. Reviewer: V.B.Marenich (Campinas) Cited in 1 ReviewCited in 3 Documents MSC: 58A17 Pfaffian systems Keywords:projective manifold; foliation; first integral × Cite Format Result Cite Review PDF Full Text: DOI References: [1] O. Calvo,Deformations of holomorphic foliations. Differential Topology, Foliations, and Group Actions, vol. 161, CONM, pp. 21-28. · Zbl 0805.32010 [2] D. Cerveau, J. F. Mattei,Formes intégrables holomorphes singulieres.97 (1982), Astérisque. · Zbl 0545.32006 [3] O. Calvo, M. Soares,Chern Numbers of a Kupka Component. Ann. Inst. Fourier,44 (1994), 1219-1236. · Zbl 0811.32024 [4] D. Cerveau, A. Lins,Codimension one Foliations in ?P n n?3, with Kupka components. Astérisque222 (1994), 93-133. · Zbl 0823.32014 [5] Ph. Griffiths, J. Harris,Principles of Algebraic Geometry. Wiley Intersc., 1978. · Zbl 0408.14001 [6] X. Gómez-Mont,Universal families of foliations by curves.150-151 (1987), Astérisque, 109-129. [7] X. Gómez-Mont, A. Lins,Structural Stability of foliations with a meromorphic first integral jour Topology.30 (1991), 315-334. · Zbl 0735.57014 [8] X. Gómez-Mont, J. Muciño,Persistent cycles for foliations having a meromorphic first integral. Holomorphic Dynamics (Gómez-Mont, Seade, Verjovsky, eds.), vol. 1345, LNM, 1987, pp. 129-162. [9] A. Medeiros,Structural stability of integrable differential forms. Geometry and Topology (M. do Carmo, J. Palis, eds.), vol. 597, LNM, 1977, pp. 395-428. [10] J. Muciño,Deformations of holomorphic foliations having a meromorphic first integral. J. Für Reine und Angewante Math (to appear). · Zbl 0816.32022 [11] M. V. Nori,Zariski’s conjecture and related topics. Ann. Scient. Ec. Normal Sup.16 (1983), 305-344. · Zbl 0527.14016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.