Question

Holomorphic function of several variables: what is the definition saying?

score 616 · Answer 1 · 2026-03-24 10:32:53

616

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Holomorphic function of several variables: what is the definition saying?

Published on 24 Mar 2026 - 10:32

score 588 · Answer 2 · 2026-03-24 10:39:20

588

Views

Is the complex tangent space closed under conjugation?

Published on 24 Mar 2026 - 10:39

score 100 · Answer 3 · 2017-03-10 18:05:24

100

Views

On a compact manifold $\Delta_{\bar\partial}(f)=0$ implies $f$ constant

Published on 10 Mar 2017 - 18:05

score 379 · Answer 4 · 2017-03-12 22:17:35

379

Views

If the base and fiber of a fiber bundle are complex manifolds, is the total space a complex manifold?

Published on 12 Mar 2017 - 22:17

score 222 · Answer 5 · 2017-03-12 23:09:38

222

Views

$S^{2n+1}\times S^{2m+1}$ is a complex manifold

Published on 12 Mar 2017 - 23:09

score 52 · Answer 6 · 2017-03-24 22:54:13

52

Views

Regularity of maps between embedded manifolds

Published on 24 Mar 2017 - 22:54

score 103 · Answer 7 · 2017-03-29 23:22:30

103

Views

A differential form generating the zero current is zero

Published on 29 Mar 2017 - 23:22

score 97 · Answer 8 · 2023-02-22 04:08:54

97

Views

What is the definition of sheaf of meromorphic differential form on a complex manifold？

Published on 22 Feb 2023 - 4:08

score 263 · Answer 9 · 2023-03-02 10:02:19

263

Views

Proof of Spherical metric on Riemann Sphere

Published on 02 Mar 2023 - 10:02

score 47 · Answer 10 · 2023-03-17 08:50:23

47

Views

Proof of the fact that $\mathfrak{g}\otimes C^{\infty}(S^1) \cong C^{\infty}(S^1;\mathfrak{g})$

Published on 17 Mar 2023 - 8:50

score 20 · Answer 11 · 2023-05-02 12:38:20

20

Views

The Fibrewise Multiplication on a Normal Vector Bundle of a subset of a Compact Kähler Surface

Published on 02 May 2023 - 12:38

score 107 · Answer 12 · 2023-05-06 10:41:07

107

Views

"Degree function" of holomorphic map between compact Riemann surfaces

Published on 06 May 2023 - 10:41

score 209 · Answer 13 · 2023-06-12 14:09:23

209

Views

Structure on a complex manifold and the Kähler form on $\mathbb{C}^2$.

Published on 12 Jun 2023 - 14:09

score 46 · Answer 14 · 2023-06-22 08:40:34

46

Views

Show that any non-trivial homogeneous polynomial $s$ of degree $k$ can be considered as a non-trivial section of $\mathcal{O}(k)$ on $\mathbb{P}^n$.

Published on 22 Jun 2023 - 8:40

score 84 · Answer 15 · 2023-08-22 08:21:49

84

Views

Basis for $T_pM^\mathbb{C}$

Published on 22 Aug 2023 - 8:21

List Question

Holomorphic function of several variables: what is the definition saying?

Is the complex tangent space closed under conjugation?

On a compact manifold $\Delta_{\bar\partial}(f)=0$ implies $f$ constant

If the base and fiber of a fiber bundle are complex manifolds, is the total space a complex manifold?

$S^{2n+1}\times S^{2m+1}$ is a complex manifold

Regularity of maps between embedded manifolds

A differential form generating the zero current is zero

What is the definition of sheaf of meromorphic differential form on a complex manifold？

Proof of Spherical metric on Riemann Sphere

Proof of the fact that $\mathfrak{g}\otimes C^{\infty}(S^1) \cong C^{\infty}(S^1;\mathfrak{g})$

The Fibrewise Multiplication on a Normal Vector Bundle of a subset of a Compact Kähler Surface

"Degree function" of holomorphic map between compact Riemann surfaces

Structure on a complex manifold and the Kähler form on $\mathbb{C}^2$.

Show that any non-trivial homogeneous polynomial $s$ of degree $k$ can be considered as a non-trivial section of $\mathcal{O}(k)$ on $\mathbb{P}^n$.

Basis for $T_pM^\mathbb{C}$

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