Natural bound in Kwiecinski's criterion for flatness
Author:
Janusz Adamus
Journal:
Proc. Amer. Math. Soc. 130 (2002), 3165-3170
MSC (2000):
Primary 14B25, 13C11
DOI:
https://doi.org/10.1090/S0002-9939-02-06422-5
Published electronically:
March 25, 2002
MathSciNet review:
1912993
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Abstract | References | Similar Articles | Additional Information
Abstract: Kwiecinski has proved a geometric criterion for flatness: A morphism of germs of analytic spaces is not flat if and only if its
fibre power
has a vertical component, for some
. We show how to bound
using Hironaka's local flattener: If
is not flat, then
has a vertical component, where
is the minimal number of generators of the ideal in
of the flattener of
.
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Additional Information
Janusz Adamus
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email:
adamus@math.toronto.edu
DOI:
https://doi.org/10.1090/S0002-9939-02-06422-5
Keywords:
Fibre product,
vertical component,
local flattener
Received by editor(s):
March 19, 2001
Received by editor(s) in revised form:
June 11, 2001
Published electronically:
March 25, 2002
Communicated by:
Wolmer V. Vasconcelos
Article copyright:
© Copyright 2002
American Mathematical Society