CR映射的形变及其应用
Deformations of CR maps and applications
摘要：
研究了正余维情形下CR映射的形变理论。特别地，我们研究了一般实子流形$M \subset \mathbb C^N$和$M' \subset \mathbb C^{N'}$之间的（非退化的芽）全纯映射$H \colon (M,p) \to M'$的{ \em映射轨迹} $E$的结构性质，定义为点集$p' \in M'$允许这样一个映射与$H(p) = p'$。我们表明，这套$E$是半解析的，并提供了例子，其中$E$拥有（规定）奇点。
英文摘要：
We study the deformation theory of CR maps in the positive codimensional case. In particular, we study structural properties of the {\em mapping locus} $E$ of (germs of nondegenerate) holomorphic maps $H \colon (M,p) \to M'$ between generic real submanifolds $M \subset \mathbb C^N$ and $M' \subset \mathbb C^{N'}$, defined to be the set of points $p' \in M'$ which admit such a map with $H(p) = p'$. We show that this set $E$ is semi-analytic and provide examples for which $E$ posseses (prescribed) singularities.
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