Z. Jelonek

activity

20182022

collaborators

13 papers

math.AG2022

Generic symmetry defect set of an algebraic curve

L. R. G. Dias, M. Farnik, Z. Jelonek

Let $X \subset C^{2 n}$ be an $n$ -dimensional algebraic variety. We define the algebraic version of the generic symmetry defect set (Wigner caustic) of $X$ . Moreover, we co…

math.AG2021

On the Fukui-Kurdyka-Paunescu Conjecture

Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio

In this paper, we prove Fukui-Kurdyka-Paunescu's Conjecture, which says that subanalytic arc-analytic bi-Lipschitz homeomorphisms preserve the multiplicities of real analytic sets.…

math.AG2021

On algebraic bi-Lipschitz homeomorphisms

Zbigniew Jelonek

Let $X \subset C^{n}; Y \subset C^{m}$ be closed affine varieties and let $ϕ : X \to Y$ be an algebraic bi-Lipschitz homeomorphism. Then $deg X = deg Y .$ Simi…

math.AG2020

A note on the Jacobian Conjecture

Zbigniew Jelonek

Let $F : C^{n} \to C^{n}$ be a polynomial mapping with a non vanishing Jacobian. If the set $S_{F}$ of non-properness of $F$ is smooth, then $F$ is a surjective mapping. Moreover,…

math.AG2020

Stability of closedness of semi-algebraic sets under continuous semi-algebraic mappings

Si Tiep Dinh, Zbigniew Jelonek, Tien Son Pham

Given a closed semi-algebraic set $X \subset R^{n}$ and a continuous semi-algebraic mapping $G : X \to R^{m},$ it will be shown that there exists an open dense s…

math.AG2020

On stable polynomial mappings

Michał Farnik, Zbigniew Jelonek

For given natural numbers $d_{1}, d_{2}$ let $Ω_{2} (d_{1}, d_{2})$ be the set off all polynomial mappings $F = (f, g) : C^{2} \to C^{2}$ such that deg $f \leq d_{1}$ , deg $g \leq d_{2}$ . We say…