Spanning subspace configurations
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866910459273150464 |
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| author | Rhoades, Brendon |
| author_facet | Rhoades, Brendon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_07579 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Spanning subspace configurations Rhoades, Brendon Combinatorics 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. |
| title | Spanning subspace configurations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1903.07579 |