Geometry and topology of generalized polygon spaces

We describe the geometry and the topology of generalized polygon spaces with “edges” in projective spaces, and fixed "edge lengths".
These spaces are symplectic quotients of degenerate co-adjoint orbits on Lie algebras, satisfying a "closing condition". They can also be viewed as moduli spaces of quiver representations of a star-shaped quiver, and as spaces of parabolic bundles over the Riemann sphere. Concentrating on the su(n) case, and using wall-crossing methods (also called flips), we obtain a recursive formula for their Poincaré polynomials.