Analytic Functions and Nonsingularity
نویسنده
چکیده
We will show that every nonsingular complex variety is a manifold in the analytic topology, but we wish to show more – that it has the natural structure of a complex manifold. In order to do this, we will need to introduce additional structure on the analytic topology. To allow for singular points, we give a definition more general than that of complex manifolds, mimicking our definitions from affine varieties and abstract varieties. With this additional structure, we will conversely be able to test nonsingularity using the analytic structure.
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