Rigid germs of finite morphisms of smooth surfaces and rational Belyi pairs

Abstract In the paper “On rigid germs of finite morphisms smooth surfaces” ( Sb. Math. , 211:10 (2020), 1354–1381), we defined a map from set $\mathcal R$?> equivalence classes branched in curves having $ADE$?> singularity types onto $\mathcal{B}el$?> rational Belyi pairs $f\colon\mathbb P^1\,{\to}\,\mathbb P^1$?> considered up to action $\mathrm{PGL}(2,\mathbb C)$?> . this article inverse images are investigated terms monodromies pairs. Bibliography: 7 titles.