Geodesic
Rigid germs of finite morphisms of smooth surfaces and rational Belyi pairs
Sbornik. Mathematics, Tome 212 (2021) no. 9, pp. 1304-1328

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In the paper “On rigid germs of finite morphisms of smooth surfaces” (Sb. Math., 211:10 (2020), 1354–1381), we defined a map $\beta\colon{\mathcal R\to\mathcal{B}el}$ from the set $\mathcal R$ of equivalence classes of rigid germs of finite morphisms branched in germs of curves having $ADE$ singularity types onto the set $\mathcal{B}el$ of rational Belyi pairs $f\colon\mathbb P^1\,{\to}\,\mathbb P^1$, considered up to the action of $\mathrm{PGL}(2,\mathbb C)$. In this article the inverse images of this map are investigated in terms of monodromies of Belyi pairs. Bibliography: 7 titles.
Keywords: rigid germs of finite covers, Belyi pairs. 
Vik. S. Kulikov. Rigid germs of finite morphisms of smooth surfaces and rational Belyi pairs. Sbornik. Mathematics, Tome 212 (2021) no. 9, pp. 1304-1328. http://geodesic.mathdoc.fr/item/SM_2021_212_9_a5/
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