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Holomorphic Vector Bundle on Hopf Manifolds with Abelian Fundamental Groups |
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| Authors: | Xiang?Yu?Zhou mailto:xyzhou@mail.math.ac.cn" title=" xyzhou@mail.math.ac.cn" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Wei?Ming?Liu |
| Affiliation: | (1) Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China;(2) Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China |
| Abstract: | Let X be a Hopf manifolds with an Abelian fundamental group. E is a holomorphic vector bundle of rank r with trivial pull-back to W = ℂ n –{0}. We prove the existence of a non-vanishing section of L⊗E for some line bundle on X and study the vector bundles filtration structure of E. These generalize the results of D. Mall about structure theorem of such a vector bundle E. The research was supported by 973 Project Foundation of China and the Outstanding Youth Science Grant of NSFC (grant no. 19825105) |
| Keywords: | Vector bundle section Hopf manifolds |
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