Natural bound in Kwiecinski’s criterion for flatness
Natural bound in Kwiecinski’s criterion for flatness
KwieciÅski has proved a geometric criterion for flatness: A morphism $f:X\to Y$ of germs of analytic spaces is not flat if and only if its $i\text {-fold}$ fibre power $f^{\{i\}} :X^{\{i\}}\to Y$ has a vertical component, for some $i$. We show how to bound $i$ using Hironakaâs local flattener: If …