We are interested in studying differential operators on algebraic
curves, with a full set of algebraic solutions. If there is no
apparent singularity, one can use the topological and combinatorial
machinery of Belyi functions and dessins d'enfants for classifying
such operators. We shall explain how to use a classical argument of
Ritter, as well as ideas of Shiga, Tsutsui and Wolfart for studying
operators having apparent singularities.