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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  1. [A] M. ARTIN, Algebraic approximation of structures over complete local rings, Publ. Math. IHES, 36 (1969), 23-58. Zbl0181.48802MR42 #3087
  2. [D] I. F. DONIN, Complete families of deformations of germs of complex spaces, Math. USSR-Sbornik, 18 (1972), 397-406. Zbl0275.32011MR48 #11574
  3. [E] R. EPHRAIM, Isosingular loci and the cartesian product structure of complex analytic singularities, Trans. Am. Math. Soc., 241 (1978), 357-371. Zbl0395.32006MR80i:32027
  4. [Fi] G. FISCHER, Complex analytic geometry, Springer Lect. Notes, 538, 1976. Zbl0343.32002MR55 #3291
  5. [FiG] W. FISCHER, H. GRAUERT, Lokal-triviale Familien kompakter komplexer Mannig-faltigkeiten, Nachr. Akad. Wiss. Göttingen, Math.-Phys. K1. II, 6 (1965), 89-94. Zbl0135.12601MR32 #1731
  6. [FIK] H. FLENNER, S. KOSAREW, On locally trivial deformations, Publ. Res. Inst. Math. Sci., 23 (1987), 627-665. Zbl0636.32010MR89c:32055
  7. [GaH] T. GAFFNEY, H. HAUSER, Characterizing singularities of varieties and of mappings, Invent. Math., 81 (1985), 427-447. Zbl0627.14004MR87m:32019
  8. [GrK] G.-M. GREUEL, U. KARRAS, Families cf varieties with prescribed singularities, Compos. Math., 69 (1989), 83-110. Zbl0684.32015MR90d:32037
  9. [H] J. E. HUMPHREYS, Linear algebraic groups, Springer, 1975. Zbl0325.20039MR53 #633
  10. [M] J. N. MATHER, Stability of C∞-mappings, III : Finitely determined map germs, Publ. Math. IHES, 35 (1968), 127-156. Zbl0159.25001MR43 #1215a
  11. [PfPo] G. PFISTER, D. POPESCU, Die strenge Approximationseigenschaft lokaler Ringe, Invent. Math., 30 (1975), 145-174. Zbl0293.13011MR52 #395
  12. [Se] A. SEIDENBERG, Analytic products, Am. J. Math., 91 (1969), 577-590. Zbl0185.49304MR40 #7261
  13. [Sc] H. W. SCHUSTER, Sur Theorie der Deformationen kompakter komplexer Räume, Invent. Math., 9 (1970), 284-294. Zbl0192.44201MR42 #3818
  14. [T] B. TEISSIER, The hunting of invariants in the geometry of discriminants, In : Real and complex singularities, Oslo 1976, 565-677. Holm, P., (ed.), Sijthoff and Noordhoff, 1977. Zbl0388.32010
  15. [V] V. S. VARADARAJAN, Lie groups, Lie algebras, and their representations, Prentice Hall, 1974. Zbl0371.22001MR51 #13113
  16. [W] J. J. WAVRIK, A theorem on solutions of analytic equations with applications to deformations of complex structures, Math. Ann., 216 (1975), 127-142. Zbl0303.32018MR52 #8488

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