Question

Unique complex structure on the modular curve $\mathbb{H}/\operatorname{PSL}(2,\mathbb{Z})$

score 154 · Answer 1 · 2019-01-14 15:46:33

154

Views

Unique complex structure on the modular curve $\mathbb{H}/\operatorname{PSL}(2,\mathbb{Z})$

Published on 14 Jan 2019 - 15:46

score 140 · Answer 2 · 2026-03-24 20:31:58

140

Views

Meromorphic Functions on Riemann Surfaces

Published on 24 Mar 2026 - 20:31

score 407 · Answer 3 · 2019-01-24 06:30:20

407

Views

Kahler metric and $(1,1)$- forms

Published on 24 Jan 2019 - 6:30

score 61 · Answer 4 · 2019-01-24 15:43:24

61

Views

What's going on when we compute $d(\gamma(z)) = \frac{1}{|cz+d|^2}dz$, where $\gamma \in \operatorname{SL}_2(\mathbb Z)$

Published on 24 Jan 2019 - 15:43

score 816 · Answer 5 · 2026-03-21 19:59:41

816

Views

Does every non-compact Riemann surface embed holomorphically into $\mathbb{C}^2$?

Published on 21 Mar 2026 - 19:59

score 453 · Answer 6 · 2026-02-23 00:47:42

453

Views

Why is the matrix representation of an almost complex structure like this?

Published on 23 Feb 2026 - 0:47

score 47 · Answer 7 · 2019-02-17 18:31:03

47

Views

Example of a complex manifold with certain qualities.

Published on 17 Feb 2019 - 18:31

score 91 · Answer 8 · 2019-02-24 23:04:58

91

Views

Compact nowhere dense analytic closed set

Published on 24 Feb 2019 - 23:04

score 20 · Answer 9 · 2026-03-22 11:35:27

20

Views

Maximum co-dimension of a submanifold given by finitely many holomorphic functions

Published on 22 Mar 2026 - 11:35

score 50 · Answer 10 · 2019-03-06 04:38:32

50

Views

Induced isomorphism between $H^{1,0}(X)$ and $H^{1,0}(Y)$ implies the induced isomorphism between $H^{0,1}(X)$ and $H^{0,1}(Y)$?

Published on 06 Mar 2019 - 4:38

score 36 · Answer 11 · 2019-03-13 22:11:47

36

Views

$\alpha\wedge\overline{\alpha}$ is nontrivial in $H^{p,p}(X)$ for a global holomorphic p-form $\alpha$

Published on 13 Mar 2019 - 22:11

score 326 · Answer 12 · 2019-03-24 17:49:50

326

Views

An almost complex structure on $M$ is equivalent to a reduction of the structure group of the tangent bundle

Published on 24 Mar 2019 - 17:49

score 92 · Answer 13 · 2019-03-30 03:27:39

92

Views

The holomorphic map from a compact smooth curve $C$ to $\mathbb{C}P^1$ when $H^0(C,\mathcal{O}(p))=2$

Published on 30 Mar 2019 - 3:27

score 81 · Answer 14 · 2019-03-31 17:09:40

81

Views

Line bundle from $\mathcal{O}(p)\cong \mathcal{O}(q)$

Published on 31 Mar 2019 - 17:09

score 1.2k · Answer 15 · 2019-04-18 16:32:06

1.2k

Views

Existence of non-constant holomorphic map between two given compact Riemann surfaces

Published on 18 Apr 2019 - 16:32

List Question

Unique complex structure on the modular curve $\mathbb{H}/\operatorname{PSL}(2,\mathbb{Z})$

Meromorphic Functions on Riemann Surfaces

Kahler metric and $(1,1)$- forms

What's going on when we compute $d(\gamma(z)) = \frac{1}{|cz+d|^2}dz$, where $\gamma \in \operatorname{SL}_2(\mathbb Z)$

Does every non-compact Riemann surface embed holomorphically into $\mathbb{C}^2$?

Why is the matrix representation of an almost complex structure like this?

Example of a complex manifold with certain qualities.

Compact nowhere dense analytic closed set

Maximum co-dimension of a submanifold given by finitely many holomorphic functions

Induced isomorphism between $H^{1,0}(X)$ and $H^{1,0}(Y)$ implies the induced isomorphism between $H^{0,1}(X)$ and $H^{0,1}(Y)$?

$\alpha\wedge\overline{\alpha}$ is nontrivial in $H^{p,p}(X)$ for a global holomorphic p-form $\alpha$

An almost complex structure on $M$ is equivalent to a reduction of the structure group of the tangent bundle

The holomorphic map from a compact smooth curve $C$ to $\mathbb{C}P^1$ when $H^0(C,\mathcal{O}(p))=2$

Line bundle from $\mathcal{O}(p)\cong \mathcal{O}(q)$

Existence of non-constant holomorphic map between two given compact Riemann surfaces

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