一类非主Hopf曲面上的全纯线丛  

Line Bundle on a Type of Non-primary Hopf Surface

作　　者：刘伟明[1] 刘亚禄[1] 苏简兵[2] 

机构地区：[1]北京石油化工学院数理部,北京102617 [2]徐州师范大学数学系,江苏徐州221116

出　　处：《厦门大学学报（自然科学版）》2005年第5期613-615,共3页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10171068);北京市优秀人才培养专项经费(20042D0500509)资助

摘　　要：非代数流形特别是非代数曲面上的全纯向量丛问题是复几何中的重要问题,近年来受到许多作者的关注.Hopf曲面是一类重要的紧的非Kahler曲面,从而是非代数的曲面.本文研究具有Abel基本群Z+Zm的非主Hopf曲面上全纯线丛,首先利用群作用的方法给出了非主Hopf曲面上全纯线丛的上同调维数的一般计算公式,然后具体给出ResonantHopf曲面上全纯线丛的上同调维数的计算结果.这些结果可用于进一步研究非主Hopf曲面上连续复向量丛全纯结构、全纯可滤结构的存在性及其分类问题.Vector Bundle on non-algebraic manifolds,especially non-algebraic surfaces,is a important problem in complex geometry. It received many authors＇ attention. Hopf surfaces is a important class of compact non-Kahlerian surfaces, then a class of compact non-algebraic surfaces. In this paper,line bundle on non-primary Hopf surfaces with Abelian fundamental group Z＋ Zm was discussed. Using the method of group action,a formula for computing the dimension of cohomology of line bundle, and the explicit results for Resonant non-primary Hopf surface were given. These results can be applied to study further the problem on the existence of a holomorphic structure or a holomorphic filtrable structure for a continuous complex vector bundle,and the classification.

关 键 词：非主Hopf曲面 线从 上同调 维数 

分 类 号：O174.56[理学—数学]