Feigin-Odesskii brackets associated with Kodaira cycles and positroid varieties
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912520214675456 |
|---|---|
| author | Hua, Zheng Polishchuk, Alexander |
| author_facet | Hua, Zheng Polishchuk, Alexander |
| contents | We establish a link between open positroid varieties in the Grassmannians $G(k,n)$ and certain moduli spaces of complexes of vector bundles over Kodaira cycle $C^n$, using the shifted Poisson structure on the latter moduli spaces and relating them to a certain twist of the standard Poisson structure on $G(k,n)$. %by a bivector field on its maximal torus. This link allows us to solve a classification problem for extensions of vector bundles over $C^n$. Based on this solution we further classify the symplectic leaves of all positroid varieties in $G(k,n)$ with respect to the twisted standard Poisson structure. Moreover, we get an explicit description of the moduli stack of symplectic leaves of $G(k,n)$ with the twisted standard Poisson structure as an open substack of the stack of vector bundles on $C^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Feigin-Odesskii brackets associated with Kodaira cycles and positroid varieties Hua, Zheng Polishchuk, Alexander Algebraic Geometry Combinatorics Quantum Algebra Representation Theory 14-XX, 22-XX, 53-XX We establish a link between open positroid varieties in the Grassmannians $G(k,n)$ and certain moduli spaces of complexes of vector bundles over Kodaira cycle $C^n$, using the shifted Poisson structure on the latter moduli spaces and relating them to a certain twist of the standard Poisson structure on $G(k,n)$. %by a bivector field on its maximal torus. This link allows us to solve a classification problem for extensions of vector bundles over $C^n$. Based on this solution we further classify the symplectic leaves of all positroid varieties in $G(k,n)$ with respect to the twisted standard Poisson structure. Moreover, we get an explicit description of the moduli stack of symplectic leaves of $G(k,n)$ with the twisted standard Poisson structure as an open substack of the stack of vector bundles on $C^n$. |
| title | Feigin-Odesskii brackets associated with Kodaira cycles and positroid varieties |
| topic | Algebraic Geometry Combinatorics Quantum Algebra Representation Theory 14-XX, 22-XX, 53-XX |
| url | https://arxiv.org/abs/2404.03935 |