On rigid germs of finite morphisms of smooth surfaces

Abstract

We prove that a germ of a finite morphism of smooth surfaces is rigid if the germ of its branch curve has one of $ADE$-singularity types and establish a correspondence between the set of rigid germs and the set of Belyi rational functions $f\in \bar{\mathbb{Q}}(z)$.

29 pages; formulation of Theorem 1 is changed

Cited by in corpus (1)

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