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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.

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Fundamental group of a compact branched cover

Ciao Francesco. The more general version of this Theorem that I know is in Fox, Ralph H. Covering spaces with singularities 1957 A symposium in honor of S. Lefschetz pp. 243–257 Princeton University …
Roberto Pignatelli's user avatar