Singular fibers in type (ii) compactified Ruijsenaars-Schneider systems are smooth connected isotropic submanifolds, diffeomorphic to S^3 over singular vertices of the action polytope in simple cases.
Audin, Torus Actions on Symplectic Manifolds, second revised edition, Birkh¨ auser, 2004
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Spherical singularities in compactified Ruijsenaars--Schneider systems
Singular fibers in type (ii) compactified Ruijsenaars-Schneider systems are smooth connected isotropic submanifolds, diffeomorphic to S^3 over singular vertices of the action polytope in simple cases.