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Results tagged with cv.complex-variables
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user 4008
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
14
votes
Accepted
Complex manifolds where bounded holomorphic functions are constant
We have that there are no non-constant bounded functions on $\mathbb C^*=\mathbb
C\setminus\{0\}$. The easiest way to see that is to notice that such a function
has a removable singularity at the orig …
- 22.6k
10
votes
Accepted
Proper holomorphic map from unit disk to punctured unit disk
I don't think so. A map $\mathbb D \to \mathbb D^\ast$ would lift to a map $\mathbb D\to \mathbb H$, where the upper halfplane $\mathbb H$ is seen as the universal cover of $\mathbb D^\ast$. As $\math …
- 22.6k
9
votes
Square of an elliptic curve and projective plane
What we have here is a special case of the following (well-known) construction:
Starting with a smooth and proper curve $C$ we may consider its symmetric power
$S^nC=C^n/\Sigma_n$. It (because we are …
- 22.6k
8
votes
Holomorphic vector fields acting on Dolbeault cohomology
These are comments on Dmitri's answer.
I don't think the surface example can work as all holomorphic forms on a compact
surface are closed (a result due to Kodaira I believe). The Cartan formula $L_v …
- 22.6k