The Structure of Vector Bundles on Non-primary Hopf Manifolds


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
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Ning GAN; Xiangyu ZHOU


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.


Hopf manifolds, Holomorphic vector bundles, Exact sequence, Cohomology, Filtration, Chern class


32L05, 32L10, 32Q55
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