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Logarithmic structure of the generalized bifurcation set

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Janeczko S.

Annales Polonici Mathematici

1996

tom 63

nr 2

187-197

Let $G: ℂ^{n} × ℂ^{r} → ℂ$ be a holomorphic family of functions. If $Λ ⊂ ℂ^{n} × ℂ^{r}$, $π_r: ℂ^{n} × ℂ^{r} → ℂ^{r}$ is an analytic variety then $Q_{Λ}(G) = {(x,u) ∈ ℂ^{n} × ℂ^{r}: G(·,u)$ has a critical point in $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 $Λ₀ = π_{r}^{-1}(0)$. In particular, we construct an algorithm for determining logarithmic stratifications provided G is versal.

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1 Annales Polonici Mathematici

1 Janeczko S.

1 1996

Wyniki wyszukiwania

Logarithmic structure of the generalized bifurcation set