Question

Is the Picard group of a smooth manifold the same as the Picard group of the associated ringed space?

score 159 · Answer 1 · 2026-03-25 09:29:00

159

Views

Is the Picard group of a smooth manifold the same as the Picard group of the associated ringed space?

Published on 25 Mar 2026 - 9:29

score 80 · Answer 2 · 2023-01-30 12:57:11

80

Views

A connected compact manifold has a unique orientable line bundle on it

Published on 30 Jan 2023 - 12:57

score 149 · Answer 3 · 2023-02-04 04:40:15

149

Views

Very ample if and only if algebra generated in degree 1?

Published on 04 Feb 2023 - 4:40

score 49 · Answer 4 · 2023-02-06 23:33:01

49

Views

Does the dual of a line bundle with no sections have a section?

Published on 06 Feb 2023 - 23:33

score 114 · Answer 5 · 2026-03-25 03:19:21

114

Views

Principal bundle (or torsor) for a diagonalizable group over a torus

Published on 25 Mar 2026 - 3:19

score 180 · Answer 6 · 2023-03-05 20:54:25

180

Views

Geometric interpretation of the isomorphism $\mathcal{N}_{Y/X} \cong \mathcal{O}_X(Y) \vert_Y$

Published on 05 Mar 2023 - 20:54

score 104 · Answer 7 · 2023-03-21 22:28:28

104

Views

Show that divisor in $\mathbb P^2\times \mathbb P^2$ is very ample.

Published on 21 Mar 2023 - 22:28

score 87 · Answer 8 · 2023-03-25 12:58:13

87

Views

Wikipedia wrong on modular forms & line bundles?

Published on 25 Mar 2023 - 12:58

score 59 · Answer 9 · 2023-03-25 13:18:45

59

Views

When determinant bundle is very ample

Published on 25 Mar 2023 - 13:18

score 133 · Answer 10 · 2023-04-07 18:33:55

133

Views

Does the first Chern class generate $H^2(P_n\mathbb{C};\mathbb{Z})$?

Published on 07 Apr 2023 - 18:33

score 25 · Answer 11 · 2026-03-25 12:50:07

25

Views

Criterion of very ampleness of $L^{\otimes 2}$ where $L$ is ample line bundle on abelian variety.

Published on 25 Mar 2026 - 12:50

score 58 · Answer 12 · 2023-04-25 09:29:04

58

Views

Parametrizing unstable extensions of line bundles

Published on 25 Apr 2023 - 9:29

score 288 · Answer 13 · 2023-04-26 03:39:18

288

Views

Triviality of line bundles

Published on 26 Apr 2023 - 3:39

score 37 · Answer 14 · 2023-05-13 04:04:17

37

Views

Why does this curve over $\mathbb{R}$ have no odd degree line bundles?

Published on 13 May 2023 - 4:04

score 85 · Answer 15 · 2023-06-07 04:17:27

85

Views

Is there a name for the following important group of line bundles with rational sections?

Published on 07 Jun 2023 - 4:17

List Question

Is the Picard group of a smooth manifold the same as the Picard group of the associated ringed space?

A connected compact manifold has a unique orientable line bundle on it

Very ample if and only if algebra generated in degree 1?

Does the dual of a line bundle with no sections have a section?

Principal bundle (or torsor) for a diagonalizable group over a torus

Geometric interpretation of the isomorphism $\mathcal{N}_{Y/X} \cong \mathcal{O}_X(Y) \vert_Y$

Show that divisor in $\mathbb P^2\times \mathbb P^2$ is very ample.

Wikipedia wrong on modular forms & line bundles?

When determinant bundle is very ample

Does the first Chern class generate $H^2(P_n\mathbb{C};\mathbb{Z})$?

Criterion of very ampleness of $L^{\otimes 2}$ where $L$ is ample line bundle on abelian variety.

Parametrizing unstable extensions of line bundles

Triviality of line bundles

Why does this curve over $\mathbb{R}$ have no odd degree line bundles?

Is there a name for the following important group of line bundles with rational sections?

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