The Quasisymmetric Grassmannian
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918470696828928 |
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| author | Bergeron, Nantel Gagnon, Lucas Spink, Hunter Tewari, Vasu |
| author_facet | Bergeron, Nantel Gagnon, Lucas Spink, Hunter Tewari, Vasu |
| contents | We construct a complex of toric varieties we call the quasisymmetric Grassmannian inside the Grassmannian of $r$-planes in $\mathbb{C}^n$. Each irreducible component is a positroid variety and an $S_n$ translate of a toric Richardson variety of ribbon shape. We describe it as the vanishing locus of equations $Δ_AΔ_{A'}=0$ in Plücker coordinates determined by a new noncrossing combinatorial object we call the quasisymmetric Johnson graph. We give an affine paving, and show that its cohomology ring is a quasisymmetric modification of the Borel presentation of the Grassmannian's cohomology, with fundamental quasisymmetric polynomials playing the role of Schur polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24903 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Quasisymmetric Grassmannian Bergeron, Nantel Gagnon, Lucas Spink, Hunter Tewari, Vasu Algebraic Geometry Combinatorics We construct a complex of toric varieties we call the quasisymmetric Grassmannian inside the Grassmannian of $r$-planes in $\mathbb{C}^n$. Each irreducible component is a positroid variety and an $S_n$ translate of a toric Richardson variety of ribbon shape. We describe it as the vanishing locus of equations $Δ_AΔ_{A'}=0$ in Plücker coordinates determined by a new noncrossing combinatorial object we call the quasisymmetric Johnson graph. We give an affine paving, and show that its cohomology ring is a quasisymmetric modification of the Borel presentation of the Grassmannian's cohomology, with fundamental quasisymmetric polynomials playing the role of Schur polynomials. |
| title | The Quasisymmetric Grassmannian |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2604.24903 |