Feigin-Odesskii brackets associated with Kodaira cycles and positroid varieties
arxiv(2024)
摘要
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 the standard Poisson structure on G(k,n). 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 standard Poisson
structure. Moreover, we get an explicit description of the moduli stack of
symplectic leaves of G(k,n) with the standard Poisson structure as an open
substack of the stack of vector bundles on C^n.
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