Positroid Links and Braid varieties
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866918297179521024 |
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| author | Casals, Roger Gorsky, Eugene Gorsky, Mikhail Simental, José |
| author_facet | Casals, Roger Gorsky, Eugene Gorsky, Mikhail Simental, José |
| contents | We study braid varieties and their relation to open positroid varieties. We discuss four different types of braids associated to open positroid strata and show that their associated Legendrian links are all Legendrian isotopic. In particular, we prove that each open positroid stratum can be presented as the augmentation variety for four different Legendrian fronts described in terms of either permutations, juggling patterns, cyclic rank matrices or Le diagrams. We also relate braid varieties to open Richardson varieties and brick manifolds, showing that the latter provide projective compactifications of braid varieties, with normal crossing divisors at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_13948 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Positroid Links and Braid varieties Casals, Roger Gorsky, Eugene Gorsky, Mikhail Simental, José Algebraic Geometry Combinatorics Geometric Topology Representation Theory Symplectic Geometry 13F60, 14M15, 53D12, 57K43 We study braid varieties and their relation to open positroid varieties. We discuss four different types of braids associated to open positroid strata and show that their associated Legendrian links are all Legendrian isotopic. In particular, we prove that each open positroid stratum can be presented as the augmentation variety for four different Legendrian fronts described in terms of either permutations, juggling patterns, cyclic rank matrices or Le diagrams. We also relate braid varieties to open Richardson varieties and brick manifolds, showing that the latter provide projective compactifications of braid varieties, with normal crossing divisors at infinity. |
| title | Positroid Links and Braid varieties |
| topic | Algebraic Geometry Combinatorics Geometric Topology Representation Theory Symplectic Geometry 13F60, 14M15, 53D12, 57K43 |
| url | https://arxiv.org/abs/2105.13948 |