Signatures and flatness.
Correction to the paper "Signatures and flatness".
An algorithmic criterion for basicness in dimension 2.
Approximation of -functions without changing their zero-set
For a function (where is a real algebraic manifold) the following problem is studied. If is an algebraic subvariety of , can be approximated by rational regular functions such that We find that this is possible if and only if there exists a rational regular function such that and g(x) for any in . Similar results are obtained also in the analytic and in the Nash cases. For non approximable functions the minimal flatness locus is also studied....
Problemi di Cousin e di Poincaré per spazi di Stein non ridotti
The Nullstellensatz for real coherent analytic surfaces.
Strata in the deformation of real isolated singularities are in general non contractible
Semialgebraicity of certain local loci
An embedding theorem for real analytic spaces
A relative embedding theorem for Stein spaces
Classification of obstructions for separation of semialgebraic sets in dimension 3.
Applying general results on separation of semialgebraic sets and spaces of orderings, we produce a catalogue of all possible geometric obstructions for separation of 3-dimensional semialgebraic sets and give some hints on how separation can be made decidable.
Smooth and analytic solutions for analytic linear systems.
We give some approximation theorems in the Whitney topology for a general class of analytic fiber bundles. This leads to a classification theorem which generalizes the classical ones.
Formal relations between quasianalytic functions of some fixed class
In [Ga] Gabrielov has given conditions under which the completion of the kernel of a morphism φ: A → B between analytic rings coincides with the kernel of the induced morphism φ̂: Â → B̂ between the completions. If B is a domain, a sufficient condition is that rk φ = dim(Â/ker φ̂), where rk φ is the rank of the jacobian matrix of φ considered as a matrix over the quotient field of B. We prove that the above property holds in a fixed quasianalytic Denjoy-Carleman class if and only if the class coincides...
Page 1