  We construct a bi-Hamiltonian structure for the holomorphic spin Sutherland
hierarchy based on collective spin variables. The construction relies on
Poisson reduction of a bi-Hamiltonian structure on the holomorphic cotangent
bundle of GL(n,C), which itself arises from the canonical symplectic structure
and the Poisson structure of the Heisenberg double of the standard GL(n,C)
Poisson--Lie group. The previously obtained bi-Hamiltonian structures of the
hyperbolic and trigonometric real forms are recovered on real slices of the
holomorphic spin Sutherland model.
