Question

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

score 160 · Answer 1 · 2026-05-10 17:39:24

160

Views

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

Published on 10 May 2026 - 17:39

score 81 · Answer 2 · 2026-03-25 14:29:58

81

Views

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

Published on 25 Mar 2026 - 14:29

score 150 · Answer 3 · 2026-03-25 14:31:38

150

Views

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

Published on 25 Mar 2026 - 14:31

score 50 · Answer 4 · 2026-03-25 14:37:35

50

Views

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

Published on 25 Mar 2026 - 14:37

score 115 · Answer 5 · 2026-05-10 14:30:24

115

Views

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

Published on 10 May 2026 - 14:30

score 181 · Answer 6 · 2026-03-25 14:36:48

181

Views

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

Published on 25 Mar 2026 - 14:36

score 105 · Answer 7 · 2026-03-25 14:37:38

105

Views

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

Published on 25 Mar 2026 - 14:37

score 88 · Answer 8 · 2026-03-25 14:32:41

88

Views

Wikipedia wrong on modular forms & line bundles?

Published on 25 Mar 2026 - 14:32

score 60 · Answer 9 · 2026-03-25 14:28:50

60

Views

When determinant bundle is very ample

Published on 25 Mar 2026 - 14:28

score 134 · Answer 10 · 2026-03-25 14:29:19

134

Views

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

Published on 25 Mar 2026 - 14:29

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 59 · Answer 12 · 2026-03-25 14:38:01

59

Views

Parametrizing unstable extensions of line bundles

Published on 25 Mar 2026 - 14:38

score 290 · Answer 13 · 2026-04-10 09:31:34

290

Views

Triviality of line bundles

Published on 10 Apr 2026 - 9:31

score 38 · Answer 14 · 2026-03-25 14:37:37

38

Views

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

Published on 25 Mar 2026 - 14:37

score 86 · Answer 15 · 2026-03-25 14:36:48

86

Views

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

Published on 25 Mar 2026 - 14:36

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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