Global positroid varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912578300542976 |
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| author | Feigin, Evgeny |
| author_facet | Feigin, Evgeny |
| contents | Positroid subvarieties of complex Grassmannians are the images of the Richardson subvarieties of the full flag varieties under the natural projection map. Positroid varieties admit natural embedding into certain quiver Grassmannians for equioriented cyclic quivers. Varying representations of the quiver, one defines global positroid varieties inside the type A global affine Grassmannian. General fiber of a family is isomorphic to the corresponding classical positroid variety and the special fiber is a subvariety of the juggling variety. We show that the global positroid families are flat and describe their (conjecturally reduced) scheme structures. We also describe the special fibers inside the product of classical positroid varieties and realize the irreducible components of the special fibers in terms of the affine Richardson varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07476 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global positroid varieties Feigin, Evgeny Algebraic Geometry Combinatorics Representation Theory Positroid subvarieties of complex Grassmannians are the images of the Richardson subvarieties of the full flag varieties under the natural projection map. Positroid varieties admit natural embedding into certain quiver Grassmannians for equioriented cyclic quivers. Varying representations of the quiver, one defines global positroid varieties inside the type A global affine Grassmannian. General fiber of a family is isomorphic to the corresponding classical positroid variety and the special fiber is a subvariety of the juggling variety. We show that the global positroid families are flat and describe their (conjecturally reduced) scheme structures. We also describe the special fibers inside the product of classical positroid varieties and realize the irreducible components of the special fibers in terms of the affine Richardson varieties. |
| title | Global positroid varieties |
| topic | Algebraic Geometry Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2509.07476 |