Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T07:03:05.924Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite Determinacy and Stability of Flatnessof Analytic Mappings

Published online by Cambridge University Press:  20 November 2018

Janusz Adamus  and
Hadi Seyedinejad
Janusz Adamus
Affiliation:
Department of Mathematics, The University of Western Ontario, London, ON, N6A and 5B7 Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8,00-956 Warsaw, poland e-mail: [email protected]
Hadi Seyedinejad
Affiliation:
Department of Mathematical Sciences, University of Kashan, Iran e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is proved that flatness of an analytic mapping germ from a complete intersection is determined by its sufficiently high jet. As a consequence, one obtains finite determinacy of complete intersections. It is also shown that flatness and openness are stable under deformations.

Keywords

58K4052K2532S0558K2032S3032B9932C0513B40finite determinacystabilityflatnessopennesscomplete intersection
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 2 , 01 April 2017 , pp. 241 - 257
Copyright
Copyright © Canadian Mathematical Society 2017

References

[1] Adamus, J. and Seyedinejad, H., Flatness testing over singular bases. Ann. Polon. Math. 107(2013), 87–96. http://dx.doi.Org/10.4064/ap107-1-6 Google Scholar
[2] Adamus, J., A fast flatness testing criterion in characteristic zero. Proc. Amer. Math. Soc. 143(2015), 2559–2570. http://dx.doi.org/10.1090/S0002-9939-2015-12463-X Google Scholar
[3] Bierstone, E. and Milman, P. D., The local geometry of analytic mappings. Dottorato di Ricerca in Matematica, ETS Editrice, Pisa, 1988.Google Scholar
[4] Douady, A., Le probléme des modules pour les sous-espaces analytiques compacts d' un espace analytique donné. Ann. Inst. Fourier (Grenoble) 16:1(1966), 1–95. http://dx.doi.Org/10.58O2/aif.226 Google Scholar
[5] Fischer, G., Complex analytic geometry. Lecture Notes in Math., 538, Springer, Berlin, Heidelberg,New York, 1976.Google Scholar
[6] Greuel, G.-M., Lossen, C., and Shustin, E., Introduction to singularities and deformations. Springer Monographs in Mathematics, Springer, Berlin, 2007.Google Scholar
[7] Hironaka, H., Stratification and flatness. Real and Complex Singularities, Proc. Oslo 1976, ed. PerHolm, Sijthoffand Noordhoff(1977), 199–265.Google Scholar
[8] Lojasiewicz, S., Introduction to complex analytic geometry. Birkhäuser, Basel, Boston, Berlin, 1991.Google Scholar
[9] Tougeron, J.-Cl., Idéaux de fonctions différentiables. Ergebnisse der Mathematik und ihrer Grenzgebiete, 71, Springer, Berlin-New York, 1972.Google Scholar