Janusz Adamus

Geometric Auslander criterion for flatness

Our aim is to understand the algebraic notion of flatness in explicit geometric terms. Let

On the holomorphic closure dimension of real analytic sets

\varphi: X \to Y

Tameness of holomorphic closure dimension in a semialgebraic set

be a morphism of complex-analytic spaces, where

A proof of Kurdyka’s conjecture on arc-analytic functions

Y

Geometric Auslander criterion for openness of an algebraic morphism

is smooth. We prove that nonflatness of

On Nash approximation of complex analytic sets in Runge domains

\varphi

Flatness testing over singular bases

is equivalent to a severe discontinuity of the fibres---the existence of a {\it vertical component} (a local irreducible component at a point of the source whose image is nowhere-dense in

Extensions of arc-analytic functions

Y

On solutions of linear equations with polynomial coefficients

)---after passage to the

Finite Determinacy and Stability of Flatness of Analytic Mappings

n