Speaker: Alexandru Chirvasitu
University at Buffalo
Will give a Algebraic Geometry and Commutative Algebra Seminar entitled:
Secant slices as symplectic leaves of moduli-space Poisson structures
Abstract: The non-commutative algebras $Q_{n,k}(E,\eta)$, introduced by Feigin and Odesskii in the course of generalizing Sklyanin's work, depend on two coprime integers $n>k\ge 1$, an elliptic curve $E$ and a point $\eta\in E$. The degeneration $\eta\to 0$ collapses $Q_{n,1}(E,\eta)$ to the polynomial ring in $n$ variables, and one obtains in this fashion a homogeneous Poisson bracket on that polynomial ring and hence a Poisson structure on the projective space $\mathbb{P}^{n-1}$. The symplectic leaves attached to that structure have received some attention in the literature, including from Feigin and Odesskii themselves and, more recently, Hua and Polishchuk. The talk revolves around various results on these symplectic leaves: their concrete description as moduli spaces of sheaf extensions on the elliptic curve $E$, the attendant realization as GIT quotients, resulting good properties (like smoothness) which follow from this without appealing to the symplectic machinery, etc. (joint with Ryo Kanda and S. Paul Smith)
Date: 11-22-2024
Time: 3:00 pm
Location: 258 Hurley Bldg