形式幂级数在复解析族形变中的应用  

Formal Power Series Applied to Deformation of Complex Analytic Family

作　　者：杨秋花 甘丽宁 卢卫君[1] 

机构地区：[1]广西民族大学数学与物理学院,广西 南宁

出　　处：《应用数学进展》2021年第5期1735-1747,共13页Advances in Applied Mathematics

摘　　要：本文主要研究紧复流形上的复解析族纤维的无穷小形变,讨论了当时复解析族的无穷小形变存在性定理。首先构造一个形式幂级数,然后应用Hölder范数与借鉴Liu-Rao-Yang关于整体典则族收敛的证明技巧证明泰勒展开式中系数的收敛性,克服了初等方法无法证明收敛性的障碍,最后给出了形变存在性定理的证明。In this paper, we study the infinitesimal deformations of complex analytic families of fibers on compact complex manifolds, and discuss the existence theorem of infinitesimal deformations of complex analytic families when . Firstly, a formal power series is constructed. Then, the convergence of the coefficients in Taylor’s expansion is proved by Hölder norm and Liu-Rao-Yang’s proof technique of global canonical family convergence, which overcomes the difficulty of proving the convergence by elementary methods. Finally, the deformation existence theorem is proved.

关 键 词：复流形 复解析族 无穷小形变 形式幂级数 H?lder范数 形式幂级数 存在性定理 

分 类 号：O17[理学—数学]