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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 …
Zhaoting Wei's user avatar
  • 9,009
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 …
Zhaoting Wei's user avatar
  • 9,009
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 …
Zhaoting Wei's user avatar
  • 9,009