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Results tagged with several-complex-variables
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user 24965
1
vote
0
answers
85
views
Do we have a Grauert-Fischer theorem for non-trivial families?
This question is related to my previous question. Let $X$ be a compact complex manifolds and $\Delta\in \mathbb{C}^n$ be a small neighborhood of $0$. A family of deformations of $X$ over $\Delta$ is a …
- 9,019
6
votes
1
answer
200
views
Do we have the Oka coherence theorem for finite group actions?
We first consider the sheaf of holomorphic functions $\mathcal{O}(\mathbb{C}^n)$ on $\mathbb{C}^n$. By Oka coherence theorem, $\mathcal{O}(\mathbb{C}^n)$ is coherent over itself.
Now we consider a fin …
- 35.2k
2
votes
0
answers
248
views
Is there a by-hand prove that $\Gamma(\mathbb{C}P^n,E)$ is finite dimensional for a holomorp...
Please let me know whether this question is suitable for Mathoverflow.
Let $E$ be a finite holomorphic vector bundle (or more generally a coherent analytic sheaf) on a compact complex manifold $X$. B …
- 6,259