A. Beauville, Complex algebraic surfaces, 1983.
DOI : 10.1017/CBO9780511623936

G. Casale, Singular codimension one foliations, Galois groupoid and first integrals, Annales de l???institut Fourier, vol.56, issue.3, pp.735-779, 2006.
DOI : 10.5802/aif.2198

D. Cerveau and A. L. Neto, Holomorphic foliations in ${\Bbb C}{\Bbb P}(2)$ having an invariant algebraic curve, Annales de l???institut Fourier, vol.41, issue.4, pp.883-903, 1991.
DOI : 10.5802/aif.1278

K. Corlette and C. Simpson, Abstract, Compositio Mathematica, vol.144, issue.05, pp.1271-1331, 2008.
DOI : 10.1112/S0010437X08003618

G. Cousin and J. V. Pereira, Transversely affine foliations on projective manifolds, Mathematical Research Letters, vol.21, issue.5, pp.985-1014, 2014.
DOI : 10.4310/MRL.2014.v21.n5.a5

A. I. Degtyarev, Quintics in CP 2 with nonabelian fundamental group, Algebra i Analiz, vol.11, issue.5, pp.130-151, 1999.

P. Deift, A. Its, A. Kapaev, and X. Zhou, On the Algebro-Geometric Integration??of the Schlesinger Equations, Communications in Mathematical Physics, vol.203, issue.3, pp.613-633, 1999.
DOI : 10.1007/s002200050037

K. Diarra, Construction et classification de certaines solutions alg??briques des syst??mes de Garnier, Construction et classification de certaines solutions algébriques des systèmes de Garnier Solutions algébriques partielles des équations isomonodromiques sur les courbes de genre 2, pp.129-154, 2013.
DOI : 10.1007/s00574-013-0006-x

A. Girand, In preparation

N. J. Hitchin, Poncelet polygons and the Painlevé equations, Geometry and analysis, pp.151-185, 1995.

M. Jimbo and T. Miwa, Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II, Phys, pp.407-448, 1981.

J. Kollàr, Rational curves on algebraic varieties, Ergebnisse der mathematik und ihrer grenzgebiete, 1999.

A. L. Neto, Some examples for the Poincaré and Painlevé problems, Ann. Sci. École Norm. Sup, vol.4, issue.35 2, pp.231-266, 2002.

F. Loray, F. Touzet, J. Vitorio, and . Pereira, Representations of quasiprojective groups, Flat connections and Transversely projective foliations, ArXiv e-prints, pp.1402-1382, 2014.

M. Mazzocco, The geometry of the classical solutions of the Garnier systems, Int. Math. Res. Not, vol.12, pp.613-646, 2002.

J. and M. Ollagnier, Liouvillian integration of the Lotka-Volterra system Liouvillian integration of the Lotka-Volterra system, Qual. Theory Dyn. Syst.Qual. Theory Dyn. Syst. Qual. Theory Dyn. Syst, vol.2, issue.5 2, pp.307-358, 2001.

B. A. Scárdua, Transversely affine and transversely projective holomorphic foliations, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.30, issue.2, pp.169-204, 1997.
DOI : 10.1016/S0012-9593(97)89918-1