  In this survey on local additive invariants of real and complex definable
singular germs we systematically present classical or more recent invariants of
different nature as emerging from a tame degeneracy principle. For this goal,
we associate to a given singular germ a specific deformation family whose
geometry degenerates in such a way that it eventually gives rise to a list of
invariants attached to this germ. Complex analytic invariants, real curvature
invariants and motivic type invariants are encompassed under this point of
view. We then explain how all these invariants are related to each other as
well as we propose a general conjectural principle explaining why such
invariants have to be related. This last principle may appear as the
incarnation in definable geometry of deep finiteness results of convex
geometry, according to which additive invariants in convex geometry are very
few.
