Normally flat ring

In algebraic geometry, a normally flat ring along a proper ideal I is a local ring A such that ${\displaystyle I^{n}/I^{n+1}}$ is flat over ${\displaystyle A/I}$ for each integer ${\displaystyle n\geq 0}$.

The notion was introduced by Hironaka in his proof of the resolution of singularities as a refinement of equimultiplicity and was later generalized by Alexander Grothendieck and others.

References

• Herrmann, M., S. Ikeda, and U. Orbanz: Equimultiplicity and Blowing Up. An Algebraic Study with an Appendix by B. Moonen. Springer Verlag, Berlin Heidelberg New-York, 1988.