一个普适放大定理III余维五以外的焦散
A Universal Magnification Theorem III. Caustics Beyond Codimension Five
摘要：
在本系列的最后一篇论文中，我们将放大不变量的结果推广到A，D，E焦散奇点的无限族。我们证明，对于家庭的一般映射之间的平面表现出任何焦散奇异的A，D，E家庭，并在目标空间中的一个点位于任何地方的区域中产生的最大数量的透镜图像（真正的前图像），总有符号的放大率的透镜图像将始终总和为零。证明是代数的性质，并依赖于欧拉迹公式。
英文摘要：
In the final paper of this series, we extend our results on magnification invariants to the infinite family of A, D, E caustic singularities. We prove that for families of general mappings between planes exhibiting any caustic singularity of the A, D, E family, and for a point in the target space lying anywhere in the region giving rise to the maximum number of lensed images (real pre-images), the total signed magnification of the lensed images will always sum to zero. The proof is algebraic in nature and relies on the Euler trace formula.
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