2011/01/10 by Janusz Adamus, Adamus, Janusz, Edward Bierstone +3
Mathematics · #32B99 #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics #Primary 13C11 #Secondary 14B25 #math.AC #math.CV #msc:13C11 #msc:14B25 #msc:32B99
paper · pdf · doi:10.48550/arxiv.1101.1938
11 pages
arxiv created 2011/01/10 · arxiv updated 2011/01/11
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.