We compute the minimal log discrepancies of determinantal varieties of square matrices, and more generally of pairs $\bigl(D^k,\sum \alpha_i D^{k_i}\bigr)$ consisting of a determinantal variety (of square matrices) and an $\mathbb R$-linear sum of determinantal subvarieties. Our result implies the semicontinuity conjecture for minimal log discrepancies of such pairs. For these computations, we use the description of minimal log discrepancies via codimensions of cylinders in the space of jets; this necessitates the computations of an explicit generator for the canonical differential forms and the Nash ideal of determinantal varieties, which may be of independent interest.

中文翻译：

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通过喷射方案的行列式变体的最小对数差异

我们计算方阵行列式变体的最小对数差异，更一般地计算由行列式变体（方阵）组成的对 $\bigl(D^k,\sum\alpha_i D^{k_i}\bigr)$ 和行列式子变量的 $\mathbb R$ 线性和。我们的结果意味着这些对的最小对数差异的半连续性猜想。对于这些计算，我们通过射流空间中圆柱的共维来使用最小对数差异的描述；这需要计算典型微分形式的显式生成器和行列簇的纳什理想，这可能是独立的兴趣。