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
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。
Abstract: 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.
文章引用：杨秋花, 甘丽宁, 卢卫君. 形式幂级数在复解析族形变中的应用[J]. 应用数学进展, 2021, 10(5): 1735-1747. https://doi.org/10.12677/AAM.2021.105185

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