Z. Jelonek

activity

20122026

most citedQuantitative properties of the non-properness set of a polynomial map

6 citations · 20 across the 22 of their papers we have counts for

collaborators

28 papers

math.CV2026

Finite holomorphic pullbacks, Segre numbers, and generic Lê numbers

Z. Jelonek, V. H. Jorge Perez, R. N. Araújo Dos Santos

We study numerical comparisons for hypersurface singularities under finite holomorphic maps between smooth germs. We retain Jelonek's topological proof of the Milnor-number inequal…

math.AG2023

The PInchuk example revisited

Filipe Fernandes, Zbigniew Jelonek

In this note we provide two special examples of non-injective polynomial maps from $R^{2}$ to $R^{2}$ with non-vanishing Jacobian: the first one is surjective, the se…

math.AG2023★ 1 cited

Bi-Lipschitz characterization of space curves

Alexandre Fernandes, Zbigniew Jelonek

In the paper \cite{renato} Renato Targino shows that bi-Lipschitz type of plane curve is determined by the local ambient topological properties of curves. Here we show that it is n…

math.CV2023

Note on Milnor numbers of irreducible germs

Zbigniew Jelonek

Let $(V, 0) \subset (C^{n}, 0)$ be a germ of a complex hypersurface and let $f : (C^{n}, 0) \to (C^{n}, 0)$ be a germ of a finite holomorphic mapping. If germs $…

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…

math.GT2020

A note on the Jacobian Conjecture

Z. Jelonek, H. Zołądek

We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.

math.GT2020

On the extension of bi-Lipschitz mappings

Lev Birbrair, Alexandre Fernandes, Zbigniew Jelonek

Let $X$ be a closed semialgebraic set of dimension $k .$ If $n \geq 2 k + 1$ , then there is a bi-Lipschitz and semialgebraic embedding of $X$ into $R^{n} .$ Moreover, if $n \geq 2 k + 2$ ,…

math.AG2019★ 1 cited

Quantitative properties of the non-properness set of a polynomial map, a positive characteristic case

Zbigniew Jelonek, Michał Lasoń

Let $f : K^{n} \to K^{m}$ be a generically finite polynomial map of degree $d$ between affine spaces. In arXiv:1411.5011 we proved that if $K$ is the fie…

math.AC2019

Elimination ideals and Bezout relations

Andre Galigo, Zbigniew Jelonek

Let $k$ be an infinite field and $I \subset k [x_{1}, \dots, x_{n}]$ be an ideal such that dim $V (I) = q$ . Denote by $(f_{1}, \dots, f_{s})$ a set of generators of $I$ . One can see that in…

math.AG2018

On finite polynomial mappings

Zbigniew Jelonek

Let $X \subset C^{n}$ be a smooth irreducible affine variety of dimension $k$ and let $F : X \to C^{m}$ be a polynomial mapping. We prove that if $m \geq k$ , then there is…

math.AG2018

Thom isotopy theorem for non proper maps and computation of sets of stratified generalized critical values

Si Tiep Dinh, Zbigniew Jelonek

Let $X \subset C^{n}$ be an affine variety and $f : X \to C^{m}$ be the restriction to $X$ of a polynomial map $C^{n} \to C^{m}$ . In this paper, we construct an affine Whitney…

math.AG2018

On quadratic polynomial mappings from the plane into the $n$ dimensional space

Michał Farnik, Zbigniew Jelonek, Piotr Migus

We show that, up to linear equivalence, there are only finitely many polynomial quadratic mappings $F : C^{2} \to C^{n}$ and $F : R^{2} \to R^{n}$ . We list all…

math.CV2016

On quadratic polynomial mappings $f : C^{2} \to C^{2}$

M. Farnik, Z. Jelonek

We show that up to linear equivalence, there is only finitely many polynomial quadratic mappings $f : C^{2} \to C^{2}$ and $f : R^{2} \to R^{2} .$ We list all possibilities.

math.AG2015★ 1 cited

Detecting asymptotic non-regular values by polar curves

Zbigniew Jelonek, Mihai Tibar

We locate the Malgrange non-regular values of a given polynomial function $f:\bC^n \to \bC$ by using a series of affine polar curves. We moreover show that all non-trivial Malgrang…

math.AG2014★ 5 cited

The set of fixed points of a unipotent group

Zbigniew Jelonek, Michał Lasoń

Let $K$ be an algebraically closed field. Let $G$ be a non-trivial connected unipotent group, which acts effectively on an affine variety $X .$ Then every non-empty component $R$ of…

math.AG2014★ 6 cited

Quantitative properties of the non-properness set of a polynomial map

Zbigniew Jelonek, Michał Lasoń

Let $f$ be a generically finite polynomial map $f : C^{n} \to C^{m}$ of algebraic degree $d$ . Motivated by the study of the Jacobian Conjecture, we prove that the set $…

math.AG2014

On the set of fixed points of a polynomial automorphism

Zbigniew Jelonek, Tomasz Lenarcik

Let K be an algebraically closed field of characteristic zero. We say that a polynomial automorphism f : K^n -> K^n is special if the Jacobian of f is equal to 1. We show that ever…

math.AG2014

On finite regular and holomorphic mappings

Zbigniew Jelonek

Let $X, Y$ be smooth algebraic varieties of the same dimension. Let $f, g : X \to Y$ be finite polynomial mappings. We say that $f, g$ are equivalent if there exists a regular auto…

math.AG2014★ 1 cited

The Thom Conjecture for proper polynomial mappings

Zbigniew Jelonek

Let $f, g : X \to Y$ be continuous mappings. We say that $f$ is topologically equivalent to $g$ if there exist homeomorphisms $Φ : X \to X$ and $Ψ : Y \to Y$ such that $Ψ\circ f\circ Φ=g.…

Finite holomorphic pullbacks, Segre numbers, and generic Lê numbers

The PInchuk example revisited

Bi-Lipschitz characterization of space curves

Note on Milnor numbers of irreducible germs

Generic symmetry defect set of an algebraic curve

On the Fukui-Kurdyka-Paunescu Conjecture

On algebraic bi-Lipschitz homeomorphisms

A note on the Jacobian Conjecture

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

On stable polynomial mappings

A note on the Jacobian Conjecture

On the extension of bi-Lipschitz mappings

Quantitative properties of the non-properness set of a polynomial map, a positive characteristic case

Elimination ideals and Bezout relations

On finite polynomial mappings

Thom isotopy theorem for non proper maps and computation of sets of stratified generalized critical values

On quadratic polynomial mappings from the plane into the n dimensional space

On quadratic polynomial mappings f:C2→C2

Detecting asymptotic non-regular values by polar curves

The set of fixed points of a unipotent group

Quantitative properties of the non-properness set of a polynomial map

On the set of fixed points of a polynomial automorphism

On finite regular and holomorphic mappings

The Thom Conjecture for proper polynomial mappings

On quadratic polynomial mappings from the plane into the $n$ dimensional space

On quadratic polynomial mappings $f : C^{2} \to C^{2}$