On germs of finite morphisms of smooth surfaces

Abstract

Questions related to deformations of germs of finite morphisms of smooth surfaces are discussed. A classification of the four-sheeted germs of finite covers $F:(U,o^{\prime })\to (V,o)$ is given up to smooth deformations, where $(U,o^{\prime })$ and $(V,o)$ are two connected germs of smooth complex-analytic surfaces. The singularity types of their branch curves and the local monodromy groups are investigated also.

Definition of D-automorphisms and several misprints are corrected