  In terms of the Interacting Boson Model, shape invariants for the ground
state, formed by quadrupole moments up to sixth order, are studied in the
dynamical symmetry limits and, for the first time, over the whole structural
range of the IBM-1. The results are related to the effective deformation
parameters and their fluctuations in the geometrical model. New signatures that
can distinguish vibrator and gamma-soft rotor structures, and one that is
related to shape coexistence, are identified.
