List questions from complex-geometry

Published on 10 May 2026 - 20:36

218

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Affine Hypersurface is a complex manifold of dimension $n - 1$

Published on 14 Apr 2026 - 0:17

78

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How to get Riemann form on complex tori

Published on 11 May 2026 - 1:25

313

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Uniformization of Riemannian Manifold with Boundary

Published on 12 Apr 2026 - 21:04

49

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Let $M$ be a complex manifold. Why are the bundles $\bigwedge^{p, q}M$ not holomorphic vector bundles over $M$ for $q \neq 0$ ?

Published on 26 Apr 2026 - 11:57

40

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Prove that the image of $f: D \rightarrow \mathbb{C}, z\mapsto\frac{i+z}{1+iz}$ is the upper half plane $H=\{z\in\Bbb{C}\mid\text{Im }z>0\}$.

Published on 14 Apr 2026 - 2:30

147

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Is $\bigwedge^{p,0}M$ a holomorphic vector bundle?

Published on 29 Apr 2026 - 12:44

59

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There are a natural number $n$ that verify $(1/5 + i (3^{1/2})/5)^n = k$; where $k$ is a real number

Published on 17 Apr 2026 - 6:37

67

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Complex structure on $\mathbb{C}P^1$

Published on 10 May 2026 - 12:29

87

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Complex Inner Product of Vectors

Published on 12 Apr 2026 - 18:01

87

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$\mathbb{R}^n$ vs $\mathbb{C}^n$ geometric intuition

Published on 11 May 2026 - 5:00

341

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(Real) holomorphic vector fields on Compact Kähler manifolds

Published on 29 Apr 2026 - 12:44

89

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Sphere minus interval is upper half plane $\mathbb{C}_{\infty} - [a \ , b] \simeq \mathcal{H}$?

Published on 17 Apr 2026 - 15:19

110

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When can you extend a holomorphic section of the Hyperplane bundle defined on a compact connected submanifold?

Published on 10 May 2026 - 15:55

143

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Question in proof of Hodge decomposition theorem

Published on 10 May 2026 - 15:07

List Question

Examples of moduli space $J$-holomorphic curves

Affine Hypersurface is a complex manifold of dimension $n - 1$

How to get Riemann form on complex tori

Uniformization of Riemannian Manifold with Boundary

Let $M$ be a complex manifold. Why are the bundles $\bigwedge^{p, q}M$ not holomorphic vector bundles over $M$ for $q \neq 0$ ?

Prove that the image of $f: D \rightarrow \mathbb{C}, z\mapsto\frac{i+z}{1+iz}$ is the upper half plane $H=\{z\in\Bbb{C}\mid\text{Im }z>0\}$.

Is $\bigwedge^{p,0}M$ a holomorphic vector bundle?

There are a natural number $n$ that verify $(1/5 + i (3^{1/2})/5)^n = k$; where $k$ is a real number

Complex structure on $\mathbb{C}P^1$

Complex Inner Product of Vectors

$\mathbb{R}^n$ vs $\mathbb{C}^n$ geometric intuition

(Real) holomorphic vector fields on Compact Kähler manifolds

Sphere minus interval is upper half plane $\mathbb{C}_{\infty} - [a \ , b] \simeq \mathcal{H}$?

When can you extend a holomorphic section of the Hyperplane bundle defined on a compact connected submanifold?

Question in proof of Hodge decomposition theorem

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