We give an explicit recipe for determining iterated local cohomology groups with support in ideals of minors of a generic matrix in characteristic zero, expressing them as direct sums of indecomposable D-modules. For non-square matrices these indecomposables are simple, but this is no longer true for square matrices where the relevant indecomposables arise from the pole order filtration associated with the determinant hypersurface. Specializing our results to a single iteration, we determine the Lyubeznik numbers for all generic determinantal rings, thus answering a question of Hochster.

中文翻译：

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行列环的迭代局部上同调群和柳贝兹尼克数

我们给出了一个明确的方法来确定迭代局部上同调群，支持特征为零的泛型矩阵的次要理想，将它们表示为不可分解 D 模的直接和。对于非方阵，这些不可分解的很简单，但对于方阵来说，情况不再如此，其中相关的不可分解来自与行列式超曲面相关的极阶过滤。将我们的结果专门用于单次迭代，我们确定了所有通用行列环的 Lyubeznik 数，从而回答了 Hochster 的问题。