V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, Grundlehrender Mathematischen Wissenschaften vol, vol.250

W. Barth, C. Peters, and A. , Van de Ven, Compact complex surfaces, 1984.

M. Belliart, I. Liousse, and F. Loray, Conformal flows on C, 0 and hexagonal 3-webs. Web theory and related topics, World Sci. Publ, pp.92-105, 1996.

J. Briançon, Extensions de Deligne pour les croisements normaux. ´ Eléments de la théorie des systèmes différentiels géométriques, pp.149-164, 2004.

R. Bryant, M. Dunajski, and M. Eastwood, Metrisability of two-dimensional projective structures, Journal of Differential Geometry, vol.83, issue.3, pp.465-499, 2009.
DOI : 10.4310/jdg/1264601033
URL : http://arxiv.org/abs/0801.0300

R. Bryant, G. Manno, and V. Matveev, A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields, Mathematische Annalen, vol.18, issue.3, pp.437-463, 2008.
DOI : 10.4310/MRL.2002.v9.n1.a5

M. Brunella, Rio de Janeiro Cartan, Sur les variétésvariétés`variétésà connexion projective, Birational Geometry of Foliations. Publicaçoes Matemáticas do IMPA. Instituto de Matemática Pura e Aplicada (IMPA), pp.52-205, 1924.

D. Dumas and I. Lect, Complex projective structures Handbook of Teichmüller theory, Math. Theor. Phys, vol.13, pp.455-508, 2009.

M. F. Luza, On the density of second order differential equations without algebraic solutions on $\mathbb{P}^2$, Publicacions Matem??tiques, vol.55, pp.163-183, 2011.
DOI : 10.5565/PUBLMAT_55111_08

M. F. Luza and F. Loray, On the number of fibrations transverse to a rational curve in complex surfaces, Comptes Rendus Mathematique, vol.354, issue.5, pp.470-474, 2016.
DOI : 10.1016/j.crma.2016.03.002
URL : https://hal.archives-ouvertes.fr/hal-01310715

M. F. Luza and P. Sad, Positive Neighborhoods of Rational Curves, Bulletin of the Brazilian Mathematical Society, New Series, vol.27, issue.1
DOI : 10.1007/BF01087535
URL : https://hal.archives-ouvertes.fr/hal-01494587

W. Fischer and H. Grauert, Lokal-triviale Familien kompakter komplexer Mannigfaltigkeiten, 14] H. Grauert, ¨ Uber Modifikationen und exzeptionelle analytische Mengen. Math. Ann, pp.89-94, 1962.

N. Hitchin, Geometrical aspects of Schlesinger's equation, Journal of Geometry and Physics, vol.23, issue.3-4, pp.287-300, 1997.
DOI : 10.1016/S0393-0440(97)80005-8

J. C. Hurtubise and N. Kamran, Projective connections, double fibrations, and formal neighbourhoods of lines, Mathematische Annalen, vol.77, issue.1, pp.383-409, 1992.
DOI : 10.1007/BF01444628

W. Kry´nskikry´nski, Webs and projective structures on a plane, Differential Geometry and its Applications, pp.133-140, 2014.

S. Kobayashi and T. Ochiai, Holomorphic projective structures on compact complex surfaces, Mathematische Annalen, vol.26, issue.1, pp.75-94, 1980.
DOI : 10.1007/BFb0069331

K. Kodaira, A Theorem of Completeness of Characteristic Systems for Analytic Families of Compact Submanifolds of Complex Manifolds, The Annals of Mathematics, vol.75, issue.1, pp.146-162, 1962.
DOI : 10.2307/1970424

S. Lie, Untersuchungen ???ber geod???tische Curven, Mathematische Annalen, vol.20, issue.3, pp.357-454, 1882.
DOI : 10.1007/BF01443601

S. R. Lebrun-jr, Spaces of complex geodesics and related structures

F. Loray, Sur les Th??or??mes I et II de Painlev??, Contemporary Mathematics, vol.389, pp.165-190, 2005.
DOI : 10.1090/conm/389/07278

I. Nakai, Curvature of curvilinear 4-webs and pencils of one forms: Variation on a theorem of Poincar???, Mayrhofer and Reidemeister, Commentarii Mathematici Helvetici, vol.73, issue.2, pp.177-205, 1998.
DOI : 10.1007/s000140050051

J. V. Pereira and L. Pirio, An invitation to web geometry, Publicações Matemáticas do IMPA. Instituto Nacional de Matemática Pura e Aplicada (IMPA), 2009.
URL : https://hal.archives-ouvertes.fr/hal-01120706

C. and I. Umr, F-35000 Rennes, France E-mail address: 1 maycolfl@gmail.com E-mail address: 2 frank.loray@univ-rennes1