Abstract
Kwiecinski has proved a geometric criterion for flatness: A morphism f: X → Y of germs of analytic spaces is not flat if and only if its i-fold fibre power f {i} : X {i} → Y has a vertical component, for some i. We show how to bound i using Hironaka's local flattener: If f is not flat, then f {d} has a vertical component, where d is the minimal number of generators of the ideal in O Y of the flattener of X.
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