3 citations · 12 across the 8 of their papers we have counts for
8 papers
On solutions of linear equations with polynomial coefficients
Janusz Adamus, Hadi Seyedinejad
We show that a linear functional equation with polynomial coefficients need not admit an arc-analytic solution even if it admits a continuous semialgebraic one. We also show that s…
Extensions of arc-analytic functions
Janusz Adamus, Hadi Seyedinejad
We prove that every arc-analytic semialgebraic function on an arc-symmetric set admits an arc-analytic semialgebraic extension to the whole ambient Euclidean space.
Decomposition of sets in real algebraic geometry
Hadi Seyedinejad
We present a new notion of decomposition of semialgebraic sets by introducing a mode of irreducibility based on arc-analytic functions. The result is a refinement of the decomposit…
A proof of Kurdyka's conjecture on arc-analytic functions
Janusz Adamus, Hadi Seyedinejad
We prove a conjecture of Kurdyka stating that every arc-symmetric semialgebraic set is precisely the zero locus of an arc-analytic semialgebraic function. This implies, in particul…
On topological classification of complex mappings
Hadi Seyedinejad
We study the topological invariant of Kwieciński and Tworzewski, particularly beyond the case of mappings with smooth targets. We derive a lower bound for of a general mapp…
Finite determinacy and stability of flatness of analytic mappings
Janusz Adamus, Hadi Seyedinejad
It is proved that flatness of an analytic mapping germ from a complete intersection is determined by its sufficiently high jet. As a consequence, one obtains finite determinacy of…
A fast flatness testing algorithm in characteristic zero
Janusz Adamus, Hadi Seyedinejad
We prove a fast computable criterion that expresses non-flatness in terms of torsion: Let R be a regular algebra of finite type over a field K of characteristic zero and let F be a…
Flatness testing over singular bases
Janusz Adamus, Hadi Seyedinejad
We show that non-flatness of a morphism f of complex-analytic spaces with a locally irreducible target Y of dimension n manifests in the existence of vertical components in the n-f…