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Logarithmic structure of the generalized bifurcation set

S. Janeczko (1996)

Annales Polonici Mathematici

Let G : n × r be a holomorphic family of functions. If Λ n × r , π r : n × r r is an analytic variety then    Q Λ ( G ) = ( x , u ) n × r : G ( · , u ) h a s a c r i t i c a l p o i n t i n Λ π r - 1 ( u ) is a natural generalization of the bifurcation variety of G. We investigate the local structure of Q Λ ( G ) for locally trivial deformations of Λ = π r - 1 ( 0 ) . In particular, we construct an algorithm for determining logarithmic stratifications provided G is versal.

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