Proceedings Of The American Mathematical Society
We construct four-dimensional symplectic orbifolds admitting Hamiltonian circle actions with isolated fixed points, but not admitting any Hamiltonian action of a two-torus. One example is linear, and one example is compact.
S. F. Singer, Janet Talvacchia, and N. Watson.
"Nontoric Hamiltonian Circle Actions On Four-Dimensional Symplectic Orbifolds".
Proceedings Of The American Mathematical Society.