Abstract
In this chapter we recall some basic facts concerning singular points of holomorphic foliations on surfaces, and in particular Seidenberg’s Theorem [39] which will play a fundamental role also in the global theory. A good reference for this material is [11].
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References
C. Camacho, P. Sad, Invariant varieties through singularities of holomorphic vector fields. Ann. Math. 115, 579–595 (1982)
C. Camacho, P. Sad, Pontos singulares de equações diferenciais analíticas, in 160 Colóquio Brasileiro de Matemática (IMPA, Rio de Janeiro, 1987)
J.-P. Jouanolou, Hypersurfaces solutions d’une équation de Pfaff. Math. Ann. 232, 239–245 (1978)
J. Martinet, J.-P. Ramis, Problèmes de modules pour des équations différentielles non linéaires du premier ordre. Publ. Math. IHES 55, 63–124 (1982)
J.-F. Mattei, R. Moussu, Holonomie et intégrales premières. Ann. Sci. ENS 13, 469–523 (1980)
A. Seidenberg, Reduction of singularities of the differential equation Ady = Bdx. Am. J. Math. 89, 248–269 (1968)
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Brunella, M. (2015). Local Theory. In: Birational Geometry of Foliations. IMPA Monographs, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-14310-1_1
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DOI: https://doi.org/10.1007/978-3-319-14310-1_1
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