English

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.

Keywords

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

R2 v1 2026-06-21T17:10:01.136Z