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2 results

  • Finite Determinacy and Stability of Flatness of Analytic Mappings

  • Janusz Adamus, Hadi Seyedinejad
  • Journal:
    Canadian Journal of Mathematics / Volume 69 / Issue 2 / 01 April 2017
    Published online by Cambridge University Press:
    20 November 2018, pp. 241-257
    Print publication:
    01 April 2017
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  • 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.

  • Stratification Theory from the Weighted Point of View

  • Toshizumi Fukui, Laurentiu Paunescu
  • Journal:
    Canadian Journal of Mathematics / Volume 53 / Issue 1 / 01 February 2001
    Published online by Cambridge University Press:
    20 November 2018, pp. 73-97
    Print publication:
    01 February 2001
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  • In this paper, we investigate stratification theory in terms of the defining equations of strata and maps (without tube systems), offering a concrete approach to show that some given family is topologically trivial. In this approach, we consider a weighted version of $\left( w \right)$-regularity condition and Kuo’s ratio test condition.