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LetG : C n ◊C r ! C be a holomorphic family of functions. If C n ◊C r , r : C n ◊ C r ! C r is an analytic variety then Q (G) ={(x,u)2 C n ◊ C r : G(·,u) has a critical point in \ 1 r (u)} is a natural generalization of the bifurcation variety ofG. We investigate the local structure of Q (G) for locally trivial deformations of 0 = 1 r (0). In particular, we construct an algorithm for determining logarithmic stratifications provided G is versal.

Logarithmic structure of the generalized bifurcation set