The strong Nagata conjecture

DOI10.1073/pnas.0308157101zbMath1065.13011OpenAlexW2143800187WikidataQ37357411 ScholiaQ37357411MaRDI QIDQ5460835

Jie-Tai Yu, Ualbei Utmakhanbetovich Umirbaev

Publication date: 19 July 2005

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://europepmc.org/articles/pmc384750

zbMATH Keywords

polynomial algebraNagata automorphismwild coordinates

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10)

Related Items

Dependence between homogeneous components of polynomials with small degree of Poisson bracket ⋮ The Jacobian Conjecture, Together with Specht and Burnside-Type Problems ⋮ Degree estimate for subalgebras generated by two elements. ⋮ On the augmentation topology of automorphism groups of affine spaces and algebras ⋮ Coordinates and automorphisms of polynomial and free associative algebras of rank three. ⋮ The Strong Anick Conjecture ⋮ TAME AUTOMORPHISMS FIXING A VARIABLE OF FREE ASSOCIATIVE ALGEBRAS OF RANK THREE ⋮ On the lifting of the Nagata automorphism ⋮ Defining relations for tame automorphism groups of polynomial rings and wild automorphisms of free associative algebras. ⋮ Test elements, retracts and automorphic orbits. ⋮ The strong Anick conjecture is true. ⋮ Generalization of an Invertible Transformation and Examples of its Applications ⋮ Degree estimate for commutators. ⋮ Automorphisms fixing a variable of \(K\langle x,y,z\rangle\). ⋮ Coordinates ofR[x,y: Constructions and Classifications]

Cites Work

• The extension of regular and rational embeddings
• Embeddings of curves in the plane
• Smooth contractible hypersurfaces in \(\mathbb{C}^ n\) and exotic algebraic structures on \(\mathbb{C}^ 3\)
• Polynomial automorphisms and Gröbner reductions
• Affine varieties with equivalent cylinders
• On the embedding dimension of an affine variety
• Length 2 variables of A[x,y and transfer]
• Poisson brackets and two-generated subalgebras of rings of polynomials
• The tame and the wild automorphisms of polynomial rings in three variables
• Tame and Wild Coordinates of 𝐾[𝑧[𝑥,𝑦]]
• The Nagata automorphism is wild