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Splicing positroid varieties

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arxiv 2405.15112 v1 pith:JN6DTED7 submitted 2024-05-24 math.AG math.CO

Eugene Gorsky , Tonie Scroggin This is my paper · ORCID
classification math.AGmath.CO
keywords circclusteropenpositroidisomorphismsubsetvarietiesapplying
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abstract

We construct an explicit isomorphism between an open subset in the open positroid variety $\Pi_{k,n}^{\circ}$ in the Grassmannian $\mathrm{Gr}(k,n)$ and the product of two open positroid varieties $\Pi_{k,n-a+1}^{\circ}\times \Pi_{k,a+k-1}^{\circ}$. In the respective cluster structures, this isomorphism is given by freezing a certain subset of cluster variables and applying a cluster quasi-equivalence.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Global positroid varieties

    math.AG 2025-09 conditional novelty 7.0 of 10

    Global positroid varieties are flat families whose general fiber is a classical positroid variety and whose special fiber is a union of affine Richardson varieties.

  2. Splicing braid varieties

    math.AG 2025-05 conditional novelty 6.0 of 10

    Open sets in braid varieties defined by transversality to a coordinate flag are isomorphic to products of two simpler braid varieties, and in the double Bott-Samelson case this splicing respects cluster structures.

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