We study local singularities of holomorphic families of arbitrary square, symmetric and skew‐symmetric matrices, that is, of mappings of smooth manifolds to the matrix spaces. Our main object is the vanishing topology of the pre‐images of the hypersurface $\mathrm{\Delta }$ of all degenerate matrices in assumption that the dimension of the source is at least the codimension of the singular locus of $\mathrm{\Delta }$ in the ambient space.

中文翻译：

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矩阵奇异性的消失循环

我们研究了任意正方形，对称和倾斜对称矩阵的全纯族的局部奇异性，即光滑流形到矩阵空间的映射。我们的主要目的是超曲面原像的消失拓扑$\mathrm{\Delta }$ 假设源的维数至少是的奇异轨迹的维数 $\mathrm{\Delta }$ 在周围的空间。