We study a holomorphic Poisson structure defined on the linear space $S(n,d):= {\rm Mat}_{n\times d}(\mathbb{C}) \times Mat}_{d\times n}(\mathbb{C})$ that is covariant under natural left actions of standard ${\rm GL}(n,\mathbb{C})$ and GL}(d,\mathbb{C})$ Poisson-Lie groups. The brackets matrix elements contain quadratic constant terms, tensor non-degenerate dense subset. Taking $d=1$ special ca...

Let X be a complex elliptic curve. In this paper we define a natural Poisson structure on the moduli spaces of stable triples (E1, E2,Φ) where E1, E2 are algebraic vector bundles on X of fixed ranks (r1, r2) and degrees (d1, d2), Φ : E2 → E1 is a homomorphism. Such triples are considered up to an isomorphism and the stability condition depends on a real parameter τ . These moduli spaces were in...

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