2024/04/05 by Zheng Hua, Hua, Zheng, Alexander Polishchuk +1
Mathematics · #14-XX #22-XX #53-XX #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2404.03935
openalex publication_date 2024/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Cn, 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 Cn. 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 Cn.