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Results tagged with complex-geometry
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user 21724
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.
15
votes
Accepted
When is the map $H^0(X,mK_X) \times H^0(X,nK_X) \to H^0(X,(m+n)K_X)$ surjective?
I assume you mean $H^0(X, K_X)^{\otimes m}$ rather than $\oplus_{i=1}^m H^0(X, K_X)$. If $X$ is a smooth projective connected complex curve of genus $g \geq 2$, then the map
$$H^0(X, K_X)^{\otimes m} …
- 7,249
25
votes
Accepted
Why is Oka's coherence theorem a deep result?
In scheme theory applied to complex geometry one usually does not encounter coherent rings which are not noetherian as well.
However if $X$ is (for example) a Stein manifold then the ring $R = \mathca …
- 7,249