Algebraic Weaves and Braid Varieties
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866910560532037632 |
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| author | Casals, Roger Gorsky, Eugene Gorsky, Mikhail Simental, José |
| author_facet | Casals, Roger Gorsky, Eugene Gorsky, Mikhail Simental, José |
| contents | In this manuscript we study braid varieties, a class of affine algebraic varieties associated to positive braids. Several geometric constructions are presented, including certain torus actions on braid varieties and holomorphic symplectic structures on their respective quotients. We also develop a diagrammatic calculus for correspondences between braid varieties and use these correspondences to obtain interesting stratifications of braid varieties and their quotients. It is shown that the maximal charts of these stratifications are exponential Darboux charts for the holomorphic symplectic structures, and we relate these strata to exact Lagrangian fillings of Legendrian links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_06931 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Algebraic Weaves and Braid Varieties Casals, Roger Gorsky, Eugene Gorsky, Mikhail Simental, José Representation Theory Algebraic Geometry Symplectic Geometry 13F60, 14M35, 53D12 In this manuscript we study braid varieties, a class of affine algebraic varieties associated to positive braids. Several geometric constructions are presented, including certain torus actions on braid varieties and holomorphic symplectic structures on their respective quotients. We also develop a diagrammatic calculus for correspondences between braid varieties and use these correspondences to obtain interesting stratifications of braid varieties and their quotients. It is shown that the maximal charts of these stratifications are exponential Darboux charts for the holomorphic symplectic structures, and we relate these strata to exact Lagrangian fillings of Legendrian links. |
| title | Algebraic Weaves and Braid Varieties |
| topic | Representation Theory Algebraic Geometry Symplectic Geometry 13F60, 14M35, 53D12 |
| url | https://arxiv.org/abs/2012.06931 |