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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.

7 votes
3 answers
614 views

Hyperbolic 3-manifolds inside algebraic varieties

I have a hyperbolic 3-manifold $M$ that I'd like to see sit inside a complex algebraic variety $V$ as beautifully and snugly as possible. I don't want to specify attributes of "beauty" (e.g., embeddin …
5 votes
1 answer
298 views

Approximation of a complex manifold by an algebraic variety

What are some natural notions of distance $d$ between two complex manifolds of dimension $n$? For any of these notions what are the current best results on approximation of a complex manifold $M$ by a …