关于嵌入复$3$ -流形的实PDMATHAAC-流形的小PDMATHAAB-扰动的复点的normal forms
On normal forms of complex points of small $\mathcal{C}^{2}$-perturbations of real $4$-manifolds embedded in a complex $3$-manifold
摘要：
本文的目的是更好地理解嵌入复$3$-流形中的实余维$2$子流形的直至二次项的复点。我们回答了一对一个任意的和一个对称的$2\times 2$矩阵关于某个线性群作用的标准形在任意小的扰动下如何变化的问题。这个结果，然后应用到描述的二次部分的规范型的复杂的点的小$\mathcal{C}^{2}$扰动的实$4$ -流形嵌入在一个复杂的$3$ -流形。
英文摘要：
The purpose of this paper is to give a better understanding of complex points up to quadratic terms of real codimension $2$ submanifolds embedded in a complex $3$-manifold. We answer the question how a normal form of a pair of one arbitrary and one symmetric $2\times 2$ matrix with respect to a certain linear group action changes under arbitrarily small perturbations. This result is then applied to describe the quadratic part of normal forms of complex points of small $\mathcal{C}^{2}$-perturbations of real $4$-manifolds embedded in a complex $3$-manifold.
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