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Normally flat ring

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


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