Geodesic
On Germs of Finite Morphisms of Smooth Surfaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 100-131

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Questions related to deformations of germs of finite morphisms of smooth surfaces are discussed. Four-sheeted finite cover germs $F: (U,o')\to (V,o)$, where $(U,o')$ and $(V,o)$ are two germs of smooth complex analytic surfaces, are classified up to smooth deformations. The singularity types of branch curves and the local monodromy groups of these germs are also investigated. 
@article{TM_2019_307_a4,
     author = {Vik. S. Kulikov},
     title = {On {Germs} of {Finite} {Morphisms} of {Smooth} {Surfaces}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {100--131},
     publisher = {mathdoc},
     volume = {307},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2019_307_a4/}
}
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Vik. S. Kulikov. On Germs of Finite Morphisms of Smooth Surfaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 100-131. http://geodesic.mathdoc.fr/item/TM_2019_307_a4/