Resolution
Global GMS
ES Strata
Build. Blocks
Comb. Appl.
HCA Proving
Arrangements
Branches
Classify
Coding
Deformations
Equidim Part
Existence
Finite Groups
Flatness
Genus
Hilbert Series
Membership
Nonnormal Locus
Normalization
Primdec
Puiseux
Plane Curves
Saturation
Solving
Space Curves
Spectrum
Flatness criterion using Fitting ideals
We consider a finitely presented A-module M:
The k-th Fitting ideal is defined as

Fk(M):= ideal generated by the n-k minors of S.

Flatness criterion:

M is flat of rank r

iff

Fr(M) = A and Fr-1(M) = 0 .
Flattening Stratification.
Application to Singularities.

KL, 06/03 http://www.singular.uni-kl.de