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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.
11
votes
Restriction of a branched cover to its branch locus
It is useful to reformulate the question in its natural differential topology setting, leaving unneeded geometric considerations aside. It is also natural to consider the analog of the problem in all …