A spanning configuration in the complex vector space \({{\mathbb {C}}}^k\) is a sequence \((W_1, \dots , W_r)\) of linear subspaces of \({{\mathbb {C}}}^k\) such that \(W_1 + \cdots + W_r = {{\mathbb {C}}}^k\). We present the integral cohomology of the moduli space of spanning configurations in \({{\mathbb {C}}}^k\) corresponding to a given sequence of subspace dimensions. This simultaneously generalizes the classical presentation of the cohomology of partial flag varieties and the more recent presentation of a variety of spanning line configurations defined by the author and Pawlowski. This latter variety of spanning line configurations plays the role of the flag variety for the Haglund–Remmel–Wilson Delta Conjecture of symmetric function theory.

甲跨越配置在复矢量空间\（{{\ mathbb {C}}} ^ķ\）是一个序列\（（W_1，\点，W_r）\）的线性子空间\（{{\ mathbb {C }}} ^ k \）这样的\（W_1 + \ cdots + W_r = {{\ mathbb {C}}} ^ k \）。我们给出\（{{\ mathbb {C}}} ^ k \）中跨度配置模空间的积分同调对应于给定子空间尺寸序列。这同时概括了部分标志变种的同调性的经典表示以及作者和Pawlowski定义的各种跨界配置的最新表示。对于对称函数理论的Haglund–Remmel–Wilson Delta猜想，后一种跨界线配置起着标志变化的作用。