CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Finite Determinacy and Stability of Flatness of Analytic Mappings

  Published:2016-04-29
 Printed: Apr 2017
  • Janusz Adamus,
    Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7
  • Hadi Seyedinejad,
    Department of Mathematical Sciences, University of Kashan, Kashan, Iran
Format:   LaTeX   MathJax   PDF  

Abstract

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: finite determinacy, stability, flatness, openness, complete intersection finite determinacy, stability, flatness, openness, complete intersection
MSC Classifications: 58K40, 58K25, 32S05, 58K20, 32S30, 32B99, 32C05, 13B40 show english descriptions Classification; finite determinacy of map germs
Stability
Local singularities [See also 14J17]
Algebraic and analytic properties of mappings
Deformations of singularities; vanishing cycles [See also 14B07]
None of the above, but in this section
Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]
Etale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]
58K40 - Classification; finite determinacy of map germs
58K25 - Stability
32S05 - Local singularities [See also 14J17]
58K20 - Algebraic and analytic properties of mappings
32S30 - Deformations of singularities; vanishing cycles [See also 14B07]
32B99 - None of the above, but in this section
32C05 - Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]
13B40 - Etale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/