On deformations of germs of finite morphisms of smooth surfaces

n the talk, questions related to deformations of germs of finite morphisms of smooth surfaces will be discussed. As example, a classification up to smooth deformations of the three-sheeted and four-sheeted germs, the singularity types of branch curves and the local monodromy groups of these germs will be given.
This work is supported by the Russian Science Foundation under grant no. 19-11-00237.