I wrote a thesis on the Grothendieck theory of dessins d'enfants (after some articles by Leila Schneps). In Shafarevich, volume 2, there's a section on real algebraic curves.
Is it possible to formulate a theory similar to that of dessins on real algebraic curves? If so, can you give me some reference (articles, papers or books)?
And, in general, may I formulate a theory of dessins on a complex manifold or on an algebraic variety of higher dimension?