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.
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This work was supported by the National Natural Science Foundation of China (Nos. 11671330, 11688101, 11431013).
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Gan, N., Zhou, X. The Structure of Vector Bundles on Non-primary Hopf Manifolds. Chin. Ann. Math. Ser. B 41, 929–938 (2020). https://doi.org/10.1007/s11401-020-0239-0
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Keywords
- Hopf manifolds
- Holomorphic vector bundles
- Exact sequence
- Cohomology
- Filtration
- Chern class
2000 MR Subject Classification
- 32L05
- 32L10
- 32Q55