Calvo-Andrade, Omegar Foliations with a Kupka component on algebraic manifolds. (English) Zbl 1058.32023 Bol. Soc. Bras. Mat., Nova Sér. 30, No. 2, 183-197 (1999). Summary: We consider codimension one holomorphic foliations in complex projective manifolds of dimension at least 3, having a compact Kupka component and represented by integrable holomorphic sections \(\omega\) of the bundle \(TM^*\otimes L\), where \(L\) denotes a very ample holomorphic line bundle. We show that, if the transversal type is not the radial vector field and \(H^1(M,\mathbb C)= 0\), then the foliation has a meromorphic first integral. Cited in 2 ReviewsCited in 7 Documents MSC: 32S65 Singularities of holomorphic vector fields and foliations 57R30 Foliations in differential topology; geometric theory Keywords:integrating factor; transversal affine structure; positive vector bundle; very ample line bundle × Cite Format Result Cite Review PDF Full Text: DOI References: [1] [C] Calvo, O.,Deformations of Branched Lefschetz Pencils. Bull. Bras. Math. Soc.26:N. 1 (1995), 67-83. · Zbl 0843.58001 · doi:10.1007/BF01234627 [2] [C-S] Calvo, O; Soares, M.,Chern Numbers of a Kupka component, Ann. Inst. Fourier44:N. 4 (1994), 1219-1236. · Zbl 0811.32024 [3] [C-L] Cerveau, D.; Lins, A., Codimension one Foliations in ??n, n ? 3, with Kupka components, Complex Analytic Methods in Dynamical Systems (C. Camacho, A. Lins, R. Mossou, P. Sad., eds.), Astérisque,222: (1994), 93-133. · Zbl 0823.32014 [4] [G-H] Griffiths Ph., Harris J.,Principles of Algebraic Geometry, Pure & Applied Math. Wiley Intersc. New York, (1978). [5] [GM-L] Gómez-Mont X.; Lins A.,Structural stability of foliations with a meromorphic first integral. Topology,30: (1990), 315-334 · Zbl 0735.57014 · doi:10.1016/0040-9383(91)90017-X [6] [Me] Medeiros A.,Structural stability of integrable differential forms, LNM 597 (J. Palis, M. do Carmo, eds.), (1977), 395-428. [7] [Sc] Scárdua, B.,Transversely Affine and Transversely Projective Foliations on Complex Projective Spaces, Ph. D. Thesis IMPA (1994). · Zbl 0889.32031 [8] [Sc1] Scárdua, B.,Transversely Affine and Transversely Projective Foliations, Ann. scient. Éc. Norm. Sup 4 e série, t. 30 (1997), 169-204. [9] [S] Schneider, M.,Über eine Vermutung von Hartshorne, Math. Ann.201: (1973), 221-229. · Zbl 0255.32009 · doi:10.1007/BF01427944 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.