Algebro-geometric methods in holomorphic distributions and foliations [1]

The theory of distributions and foliations has its origins in

the studies of nineteenth-century mathematicians such as

Grassmann, Jacobi, Clebsch, Cartan and Frobenius. They

were motivated by the fundamental work due to Pfaff, who

proposed a geometric approach to the study of differen-

tial equations. Distributions and foliations play an impor-

tant role in several subjects from differential, complex, al-

gebraic and Poisson geometries. The qualitative study of fo-

liations induced by complex polynomial differential equa-

tions was investigated by Poincare', Darboux and Painleve'.