The trivial locus of an analytic map germ

H. Hauser; G. Muller

Annales de l'institut Fourier (1989)

  • Volume: 39, Issue: 4, page 831-844
  • ISSN: 0373-0956

Abstract

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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 .

How to cite

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Hauser, H., and Muller, G.. "The trivial locus of an analytic map germ." Annales de l'institut Fourier 39.4 (1989): 831-844. <http://eudml.org/doc/74858>.

@article{Hauser1989,
abstract = {We prove: For a local analytic family $\lbrace X_s\rbrace _\{s\in S\}$ 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 $X_0$.},
author = {Hauser, H., Muller, G.},
journal = {Annales de l'institut Fourier},
keywords = {morphisms of analytic space germs; cartesian products; deformations},
language = {eng},
number = {4},
pages = {831-844},
publisher = {Association des Annales de l'Institut Fourier},
title = {The trivial locus of an analytic map germ},
url = {http://eudml.org/doc/74858},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Hauser, H.
AU - Muller, G.
TI - The trivial locus of an analytic map germ
JO - Annales de l'institut Fourier
PY - 1989
PB - Association des Annales de l'Institut Fourier
VL - 39
IS - 4
SP - 831
EP - 844
AB - We prove: For a local analytic family $\lbrace X_s\rbrace _{s\in S}$ 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 $X_0$.
LA - eng
KW - morphisms of analytic space germs; cartesian products; deformations
UR - http://eudml.org/doc/74858
ER -

References

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