|
|
| |
| The Structure of Vector Bundles on Non-primary Hopf Manifolds∗ |
| |
Citation： |
Ning GAN,Xiangyu ZHOU.The Structure of Vector Bundles on Non-primary Hopf Manifolds∗[J].Chinese Annals of Mathematics B,2020,41(6):929~938 |
| Page view： 710
Net amount： 458 |
Authors： |
Ning GAN; Xiangyu ZHOU |
Foundation： |
This work was supported by the National Natural Science Foundation of China (Nos. 11671330,11688101, 11431013). |
|
|
| Abstract： |
Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X, with trivial pull-back to Cn ? {0}. The authors show that there exists a line bundle L over X such that E ? L has a nowhere vanishing section. It is proved that in case dim(X) ≥ 3, π?(E) is trivial if and only if E is filtrable by vector bundles. With the structure theorem, the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E. |
Keywords： |
Hopf manifolds, Holomorphic vector bundles, Exact sequence, Cohomology, Filtration, Chern class |
Classification： |
32L05, 32L10, 32Q55 |
|
|
Download PDF Full-Text
|
|
|
|
