Finite determinacy and stability of flatness of analytic mappings
Janusz Adamus, Hadi Seyedinejad
TL;DR
This paper proves that the flatness of analytic mappings from complete intersections is determined by finite jets, establishing finite determinacy and stability of flatness and openness under deformations.
Contribution
It introduces the finite determinacy of flatness for analytic mappings from complete intersections and demonstrates the stability of flatness and openness under deformations.
Findings
Flatness is determined by sufficiently high jets.
Finite determinacy of complete intersections is established.
Flatness and openness are stable under deformations.
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.
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