The trivial locus of an analytic map germ
Annales de l'Institut Fourier, Tome 39 (1989) no. 4, pp. 831-844.

On prouve : Toute famille locale analytique {X s } s∈S de germes d’espaces analytiques admet un plus grand sous-espace T de S au-dessus duquel elle soit triviale. En plus, la réduction de T est égale au germe des points s de S tels que X, soit isomorphe à la fibre spéciale X 0 .

We prove: For a local analytic family {X s } s∈S of analytic space germs there is a largest subspace T in S such that the family is trivial over T. Moreover the reduction of T equals the germ of those points s in S for which X s is isomorphic to the special fibre X 0 .

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     title = {The trivial locus of an analytic map germ},
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Hauser, H.; Muller, G. The trivial locus of an analytic map germ. Annales de l'Institut Fourier, Tome 39 (1989) no. 4, pp. 831-844. doi : 10.5802/aif.1191. http://archive.numdam.org/articles/10.5802/aif.1191/

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