Some Results on Holomorphic Vector Bundles Over General Hopf Manifolds  

作　　者：甘宁 周向宇 

机构地区：[1]Institute of Mathematics Academy of Mathematics and Systems Sciences,Chinese Academy of Sciences,Beijing,100080,P.R.China

出　　处：《数学进展》2005年第2期245-248,共4页Advances in Mathematics（China）

基　　金：Foundation item: This research is supported by the National Natural Science Foundation of P. R. China(No.10071048).

摘　　要：1 Introduction In recent years, holomorphic vector bundles on non-algebraic manifolds received increased attention[2]. The main problem is to determine which continuous complex vector bundle carries a holomorphic structure or furthermore a holomorphic filtrable structure. D. Mall studied vector bundles on the primary Hopf manifolds[s-ii]. Zhou and Liu studied the Hopf manifolds with Abelian fundamental group[7,i4]. Here we study the Hopf manifolds with Non-Abelian fundamental group π1 (X) ≌ Z. H. We use the generalized Douady sequence obtained in [13] and use the method of group action to get the formula for computing of dimensions of cohomology of line bundles on non-primary Hopf manifold, especially non-primary Hopf surfaces. Then using the same method, get the formula for computing of dimensions of cohomology of holomorphic vector bundles with trivial pull-back on non-primary Hopf manifold, and get the filtrable property and the Structure Theorem.

关 键 词：正则复向量丛 连续性 霍普夫非代数流形 过滤结构 阿贝尔群 

分 类 号：O152.2[理学—数学]