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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.

2 votes
0 answers
238 views

When is the analytification of a variety homeomorphic to $\mathbb C$

Let $X$ be the analytification of a variety $V$ such that $X$ is homeomorphic to $\mathbb R^2$. What can we say about $X$? Can $V$ be singular?
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9 votes
1 answer
497 views

Is the number of minimal models finite

Let $X$ be a variety of general type. Assume that $\dim X = 3$. In https://eudml.org/doc/164223 it is proven that $X$ has only finitely many minimal models (i.e., only $\mathbb Q$-factorial terminal …
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