Timeline for Building all holomorphic vector bundles from the tangent bundle
Current License: CC BY-SA 4.0
15 events
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S Jul 4, 2020 at 11:08 | history | bounty ended | CommunityBot | ||
S Jul 4, 2020 at 11:08 | history | notice removed | CommunityBot | ||
Jun 26, 2020 at 12:29 | comment | added | Libli | If you assume that the canonical bundle is ample or anti-ample, then I think your question has an affirmative answer. As you noticed, the determinant of the tangent bundle is a sub-bundle of the $n$-th ($n = \dim V$) power of the tangent bundle. Up to a dual, you get an ample line bundle. Now, up to some twists by this ample line bundle, every vector bundle is a quotient of a trivial vector bundle (global generation up to twists). | |
Jun 26, 2020 at 12:15 | comment | added | abx | It's not a good idea to change completely a question when there are already comments and answers. | |
S Jun 26, 2020 at 9:33 | history | bounty started | CommunityBot | ||
S Jun 26, 2020 at 9:33 | history | notice added | user145520 | Improve details | |
Jun 24, 2020 at 15:37 | history | edited | user145520 | CC BY-SA 4.0 |
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Jun 24, 2020 at 15:25 | comment | added | Jason Starr | If you also allow direct sums, the rephrased question has a positive answer for all compact (connected) Riemann surfaces of genus $g\neq 1$. | |
Jun 24, 2020 at 15:23 | history | became hot network question | |||
Jun 24, 2020 at 12:01 | history | edited | user145520 | CC BY-SA 4.0 |
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Jun 24, 2020 at 8:21 | history | edited | user145520 | CC BY-SA 4.0 |
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Jun 24, 2020 at 8:08 | comment | added | Piotr Achinger | Vector bundles on $\mathbb{P}^n$ have continuous moduli for $n>1$. Every projective variety admits a finite morphism $X\to \mathbb{P}^{\dim X}$, so the same should hold for $X$. It therefore seems that examples of the kind you want do not exist among projective varieties (and perhaps also among proper algebraic varieties). | |
Jun 24, 2020 at 8:05 | answer | added | Sasha | timeline score: 9 | |
Jun 24, 2020 at 7:59 | history | edited | user145520 | CC BY-SA 4.0 |
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Jun 24, 2020 at 7:23 | history | asked | user145520 | CC BY-SA 4.0 |