For a toric integrable Hamiltonian system (IHS) with n degrees of freedom, the image of the moment map F is a n-dimensional rational convex polytope.
This is no longer the case when we deal with semi-toric IHS. Yet we can recover a nice description of the image of the moment map for these systems. This requires a good description of the locci of semi-toric critical values.
One way of doing so is by using the local model existing for
