An inductive analytic criterion for flatness
Commutative Algebra
2011-01-11 v1 Complex Variables
Abstract
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 codimension zero" and a condition "in codimension one" which can be used together with the Weierstrass preparation theorem to inductively reduce the fibre dimension of the morphism.
Cite
@article{arxiv.1101.1938,
title = {An inductive analytic criterion for flatness},
author = {Janusz Adamus and Edward Bierstone and Pierre D. Milman},
journal= {arXiv preprint arXiv:1101.1938},
year = {2011}
}
Comments
11 pages