Stable map quotients (and orbifold log resolutions) of Richardson varieties
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913838637514752 |
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| author | Knutson, Allen |
| author_facet | Knutson, Allen |
| contents | Let $X_λ^μ:= X_λ\cap X^μ\subseteq G/P$ be a Richardson variety in a generalized partial flag manifold. We use equivariant stable map spaces to define a canonical resolution $\widetilde{X_λ^μ}$ of singularities, albeit obtaining an orbifold not a manifold. The ``nodal curves'' boundary is an (orbifold) simple normal crossings divisor, and is conjecturally anticanonical. Its dual simplicial complex is the order complex of the open Bruhat interval $(λ,μ) \subseteq W/W_P$, shown in [Björner-Wachs '82] to be a sphere or ball. In the case of $G/P$ a Grassmannian, the resolution $\widetilde{X_λ^μ}$ is a GKM space, whose $T$-fixed points are indexed by rim-hook tableaux. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09905 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable map quotients (and orbifold log resolutions) of Richardson varieties Knutson, Allen Algebraic Geometry 14M15 14H10 Let $X_λ^μ:= X_λ\cap X^μ\subseteq G/P$ be a Richardson variety in a generalized partial flag manifold. We use equivariant stable map spaces to define a canonical resolution $\widetilde{X_λ^μ}$ of singularities, albeit obtaining an orbifold not a manifold. The ``nodal curves'' boundary is an (orbifold) simple normal crossings divisor, and is conjecturally anticanonical. Its dual simplicial complex is the order complex of the open Bruhat interval $(λ,μ) \subseteq W/W_P$, shown in [Björner-Wachs '82] to be a sphere or ball. In the case of $G/P$ a Grassmannian, the resolution $\widetilde{X_λ^μ}$ is a GKM space, whose $T$-fixed points are indexed by rim-hook tableaux. |
| title | Stable map quotients (and orbifold log resolutions) of Richardson varieties |
| topic | Algebraic Geometry 14M15 14H10 |
| url | https://arxiv.org/abs/2505.09905 |