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arXiv · 1903.07579

Spanning subspace configurations

Brendon Rhoades
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Abstract

A {\em 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.

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Brendon Rhoades. 2019-03-18. Spanning subspace configurations. https://arxiv.org/abs/1903.07579

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