List questions from line-bundles

Published on 26 Apr 2021 - 16:34

174

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Any smooth complex line bundle over a smooth manifold is a subbundle of a trivial bundle

Published on 26 May 2021 - 16:31

221

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Over a general field, does $h^1(X,\mathcal{O}_X)=0$ imply $\text{Pic}(X)\simeq \text{NS}(X)$?

Published on 10 Jun 2021 - 19:32

371

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Line subbundles of tangent bundle of a manifold is trivial?

Published on 23 Jun 2021 - 1:11

218

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Why are Cousin problems so relevant?

Published on 25 Mar 2026 - 23:17

175

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Pulling back divisors and example 7.6.3 in Hartshorne

Published on 13 Jul 2021 - 19:05

201

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Line bundles on complete flag varieties independent of isogeny class

Published on 03 Aug 2021 - 15:48

47

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pseudoeffctive holomorphic line bundle with trivial Chern class

Published on 12 Aug 2021 - 19:05

101

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Question about the (exactness of the) curvature form of a Hermitian metric

Published on 13 Aug 2021 - 11:42

179

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Global section of the line bundle ${\cal O}_{{\Bbb P}_k}(1)$ over ${\Bbb P}_k^1$.

Published on 17 Aug 2021 - 15:28

70

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Determinant of the vertical tangent bundle of a projectivised bundle

Published on 26 Mar 2026 - 1:11

39

Views

Explicit correpsondence between ${\cal O}_{{\Bbb P}_k^1}(1) = {\cal O}_{{\Bbb P}_k^1}(x)$.

Published on 17 Aug 2021 - 17:03

42

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$c_1^2(L)\geq 0$ for a nef line bundle $L\to S$ over a complex surface

Published on 25 Mar 2026 - 14:22

219

Views

Global sections of a line bundle vanishing on a subvariety

Published on 15 Sep 2021 - 16:18

262

Views

Very ample line bundle and the induced embedding

Published on 23 Sep 2021 - 19:57

List Question

Existence of a global section of $L(D)$ vanishing on $D$.

Any smooth complex line bundle over a smooth manifold is a subbundle of a trivial bundle

Over a general field, does $h^1(X,\mathcal{O}_X)=0$ imply $\text{Pic}(X)\simeq \text{NS}(X)$?

Line subbundles of tangent bundle of a manifold is trivial?

Why are Cousin problems so relevant?

Pulling back divisors and example 7.6.3 in Hartshorne

Line bundles on complete flag varieties independent of isogeny class

pseudoeffctive holomorphic line bundle with trivial Chern class

Question about the (exactness of the) curvature form of a Hermitian metric

Global section of the line bundle ${\cal O}_{{\Bbb P}_k}(1)$ over ${\Bbb P}_k^1$.

Determinant of the vertical tangent bundle of a projectivised bundle

Explicit correpsondence between ${\cal O}_{{\Bbb P}_k^1}(1) = {\cal O}_{{\Bbb P}_k^1}(x)$.

$c_1^2(L)\geq 0$ for a nef line bundle $L\to S$ over a complex surface

Global sections of a line bundle vanishing on a subvariety

Very ample line bundle and the induced embedding

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