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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Simple birational extensions of the polynomial algebra C[3]
- 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…