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Results tagged with vector-bundles
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user 3377
A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.
8
votes
Accepted
Does it make sense to define a holomorphic structure on $\mathbb{C}P^\infty$ and vector bund...
Yes, there is lots of literature on this subject.
However, Tyurin proved that all vector bundles on $CP^\infty$ are
direct sum of line bundles. There are several more recent papers by
Penkov and Tikho …
- 9,237
5
votes
Extending vector bundles from subvarieties
An obvious obstruction comes from topology: the Chern classes of your
bundle should be obtained from restriction of Hodge classes on an ambient variety. This is (more or less) enough to extend a smoo …
- 9,237
3
votes
top chern class
Take a Hopf surface $H$, projected to ${\Bbb C}P^1$ with fibers elliptic curves, and let $L=\pi^* O(1)$ be a pullback of $O(1)$ from ${\Bbb C}P^1$ to $H$. Since $H=S^3\times S^1$, all line bundles are …
- 9,237
2
votes
Projectively flat Hermitian curvature proportional to Kähler form?
The curvature form of any bundle is closed by Bianchi identity, hence
your form $s\omega$ is necessarily closed. This implies that $s=const$, unless $dim_C M=1$, because $ds\wedge \omega=0$ implies $ …
- 9,237