Abstract
In this chapter we start the global study of foliations on complex surfaces. The most basic global invariants which may be associated with such a foliation are its normal and tangent bundles, and here we shall prove several formulae and study several examples concerning the calculation of these bundles. We shall mainly follow the presentation given in [5]; the book [20] may also be of valuable help.
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References
W. Barth, C. Peters, A. Van de Ven, Compact Complex Surfaces (Springer, Heidelberg, 1984)
M. Brunella, Feuilletages holomorphes sur les surfaces complexes compactes. Ann. Sci. ENS 30, 569–594 (1997)
M. Brunella, Some remarks on indices of holomorphic vector fields. Publ. Matemàtiques 41, 527–544 (1997)
R. Friedman, Algebraic Surfaces and Holomorphic Vector Bundles (Springer, New York, 1998)
X. Gomez-Mont, L. Ortiz-Bobadilla, Sistemas dinamicos holomorfos en superficies. Aportaciones matematicas (Soc. Mat. Mexicana, México, 1989)
Ph. Griffiths, J. Harris, Principles of Algebraic Geometry (Wiley, New York, 1978)
F. Serrano, Fibred surfaces ad moduli. Duke Math. J. 67, 407–421 (1992)
T. Suwa, Indices of Vector Fields and Residues of Holomorphic Singular Foliations (Hermann, Paris, 1998)
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Brunella, M. (2015). Foliations and Line Bundles. In: Birational Geometry of Foliations. IMPA Monographs, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-14310-1_2
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DOI: https://doi.org/10.1007/978-3-319-14310-1_2
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