## 12 Citations

### Bivariables and Vénéreau polynomials

- MathematicsAnnales de la Faculté des sciences de Toulouse : Mathématiques
- 2022

— We study a family of polynomials introduced by Daigle and Freudenburg, which contains the famous Vénéreau polynomials and defines A2fibrations over A2. According to the Dolgachev–Weisfeiler…

### Strongly Residual Coordinates over A [ x ]

- Mathematics
- 2014

For a commutative ring A, a polynomial f ∈ A[x][n] is called a strongly residual coordinate if f becomes a coordinate (over A) upon going modulo x, and f becomes a coordinate (over A[x, x −1]) upon…

### Bivariables and V\'en\'ereau polynomials.

- Mathematics
- 2020

We study a family of polynomials introduced by Daigle and Freudenburg, which contains the famous Venereau polynomials and defines $\mathbb{A}^2$-fibrations over $\mathbb{A}^2$. According to the…

### FAMILIES OF GROUP ACTIONS, GENERIC ISOTRIVIALITY, AND LINEARIZATION

- Mathematics
- 2012

Our base field is the field ℂ of complex numbers. We study families of reductive group actions on $$ {\mathbb A} $$2 parametrized by curves and show that every faithful action of a non-finite…

### Closed polynomials and their applications for computations of kernels of monomial derivations

- MathematicsJournal of Algebra
- 2019

### The cancellation problem over Noetherian one-dimensional domains

- Mathematics
- 2014

LetR be a commutative Noetherian one-dimensional domain containingQ. In this paperweprove that if anR-algebraA is such thatA[n] ∼=R R[n+2], for somen≥ 1, then A ∼=R R[2]. In terms of affine…

### The epimorphism theorem and its generalizations

- Mathematics
- 2015

The celebrated "Epimorphism Theorem" opened up several directions of research. In this survey article we highlight the known partial results and open questions on (i) the epimorphism problem for…

### A unified approach to embeddings of a line in 3-space

- Mathematics
- 2022

While the general question of whether every closed embedding of an affine line in affine 3-space can be rectified remains open, there have been several partial results proved by several different…

### Interpolation in the Automorphism Group of a Polynomial Ring

- Mathematics
- 2020

Let R be a commutative ring with unity and SAn(R) be the group of volume-preserving automorphisms of the polynomial R-algebra R[n]. Given a proper ideal 𝔞 of R, we address in this paper the question…

### $\mathbb{A}^2$ -Fibrations between affine spaces are trivial $\mathbb{A}^2$-bundles

- Mathematics
- 2017

We give a criterion for a flat fibration with affine plane fibers over a smooth scheme defined over a field of characteristic zero to be a Zariski locally trivial $\mathbb{A}^2$-bundle. An…

## References

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- Mathematics
- 2001

The Abhyankar-Sathaye Problem asks whether any biregular embedding φ: C k → C n can be rectified, that is, whether there exists an automorphism a E Aut C n such that a o φ is a linear embedding. Here…

### Polynomial coordinates and their behavior in higher dimensions

- Mathematics
- 2004

A coordinate is an element of a polynomial ring which is the first component of some automorphism of this ring. Understanding the structure of coordinates is still one of the major problems in the…

### Locally polynomial algebras are symmetric algebras

- Mathematics
- 1976

of a finitely generated projective K-module P. This result, to which the title refers, is contained in Theorem (4.4) below. Geometrically it asserts that every locally trivial fibre space over…

### The special automorphism group of R[t]/(tm)[x1,…,xn]R[t]/(tm)[x1,…,xn] and coordinates of a subring of R[t][x1,…,xn]R[t][x1,…,xn]

- Mathematics
- 2007

### Families of Affine Fibrations

- Mathematics
- 2010

This paper gives a method of constructing affine fibrations for polynomial rings. The method can be used to construct the examples of \(\mathbb {A}\) 2-fibrations in dimension 4 due to Bhatwadekar…

### Automorphismes et variables de l'anneau de polynômes A[y_1,...,y_n]

- Physics
- 2001

Dans un anneau de polynomes a $n$ indeterminees $A\n=A[y_1\tr y_n]$ a coefficients dans un anneau commutatif unitaire $A$ on dit qu'un polynome $p=p(y_1\tr y_n)$ est une variable ou $A$-variable s'il…