Main references
 
Kevin Corlette, Carlos Simpson. On the classification of rank-two representations of quasiprojective fundamental groups. Compos. Math. 144 (2008), no. 5, 1271–1331.
Mathscinet         zbMATH              Journal                arXiv
 
Jean-Pierre Demailly. On the Frobenius integrability of certain holomorphic p-forms. Complex geometry (Göttingen, 2000), 93–98, Springer, Berlin, 2002.
Mathscinet         zbMATH              Journal                 arXiv
 
Frédéric Touzet. On the structure of codimension 1 foliations with pseudoeffective conormal bundle. Foliation theory in algebraic geometry, 157–216, Simons Symp., Springer, Cham, 2016.
Mathscinet         zbMATH              Journal                arXiv
 
Frédéric Touzet. Uniformisation de l’espace des feuilles de certains feuilletages de codimension un. Bull. Braz. Math. Soc. (N.S.) 44 (2013), no. 3, 351–391.
Mathscinet         zbMATH              Journal                 arXiv
 
Textbook
 
Marco Brunella. Birational geometry of foliations. IMPA Monographs, 1. Springer, Cham, 2015. xiv+130 pp. 
Mathscinet         zbMATH
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