7 papers
On Buzzard's Theoren
Zbigniew Jelonek, Gustavo Menani, Maria Michalska
Over any infinite field we prove existence of polynomial automorphism with prescribed differentials at points. More precisely, let $\K$ be an infinite field and …
On mappings with Jacobian one
Zbigniew Jelonek
We show that the set of polynomial automorphisms of degree at most and with is Zariski closed. In particular every irreducib…
Lipschitz embeddings of algebraic curves
Zbigniew Jelonek, Gustavo Menani, Maria Michalska
We show that inner Lipschitz classification of real algebraic curves is equivalent to outer Lipschitz classification in of real algebraic curves with LNE connected c…
Proof of the metric Arnold's corank problem
Aexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio
In this article, we approach the Arnold corank problem, posed by Arnold in 1975, which asks whether the corank of holomorphic functions is an ambient topological invariant. Here, w…
On metric equivalence of the Brieskorn-Pham hypersurfaces
Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio
We show that two bi-Lipschitz equivalent Brieskorn-Pham hypersurfaces have the same multiplicities at . Moreover we show that if two algebraic -dimensional cones $P, R\su…
Bi-Lipschitz equivalent cones with different degrees
Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio
We show that for every there exist complex algebraic cones of dimension with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but they…
On real polynomial local homeomorphisms
Alexandre Fernandes, Zbigniew Jelonek
We prove that the set of non-properness of a polynomial mapping of the three dimensional space which is a local homeomorphism cannot be homeomorphic to the real line