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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.

3 votes
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Let $f: X \to D$ be a proper holomorphic submersion. Does a holomorphic form on $X$, closed ...

Let $D$ be the unit disc in $\mathbb{C}^n$ and let $f: X \to D$ be a proper surjective holomorphic submersion, which is trivial as a smooth fiber bundle, with connected fiber $F$. We get an induced fl …
1 vote

Holomorphic Gauss normal map

Let $S$ be the embedded surface (assumed compact and not homeomorphic to a sphere) and let $S_1$ and $S_2$ be the subsets of $S$ where the Gaussian curvature is positive and negative, respectively. By …
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