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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?

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  • $\begingroup$ Perhaps you can post this on mathoverflow? you might get some better responses there. Maybe ask a moderator to move it over there. $\endgroup$ – Robert Cardona Feb 20 '15 at 20:51
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I don't know if you are still interested by the subject. Real dessins d'enfant is a really interesting subject, and first introduced in this article.

The idea is simple : instad of looking the preimage of $[0,1]$, one should look at the preimage of $\mathbb RP^1$, and putting extra "real" decoration.

A full book on the subject is here with lot of informations and applications. Real dessin d'enfants can give lot of informations about singular curves (computation of their fundamental group), and also Lefschetz fibrations.

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