Related papers: Geometric Auslander criterion for flatness

This paper has been withdrawn by the author due to an error in the proof of Proposition 4.8.

%auto-ignore This paper has been withdrawn by the author, due to a crucial error.

This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.

This paper has been withdrawn

Paper withdrawn due to a crucial algebraic error in section 3.

This paper is withdrawn.

This paper has been withdrawn by the author due to an error.

This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.

This paper has been withdrawn to allow publication elsewhere.

Paper withdrawn because of unjustified approximation between equations 13 and 14.

We present a constructive criterion for flatness of a morphism of analytic spaces X -> Y or, more generally, for flatness over Y of a coherent sheaf of modules on X. The criterion is a combination of a simple linear-algebra condition "in…

This paper has been withdrawn by the authors due to a gap in the proof of the main result (in 5.3).

This paper has been withdrawn by the author. It will be replaced, substantially modified, by sections of the author's completed PhD thesis.

This paper has been withdrawn by the authors.

This article is withdrawn because of a mistake in the main result of the paper.

This paper has been withdrawn by the author due to a crucial error in the proofs. The error has been corrected and the paper has been expanded in arXiv:0910.5327

Paper withdrawn due to an error into the equations of the probability amplitudes.

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

This article has been withdrawn due to an error in a proof of the main result.

This paper has been withdrawn by the author, due to an error in relation (11).