Embeddings of hypersurfaces in affine spaces.

zbMath1064.14076arXivmath/0010211MaRDI QIDQ5942790

Vladimir Shpilrain, Jie-Tai Yu

Publication date: 2001

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0010211

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10) Hypersurfaces and algebraic geometry (14J70)

Related Items

Affine varieties with equivalent cylinders ⋮ Embeddings of a family of Danielewski hypersurfaces and certain \(\mathbb C^+\)-actions on \(\mathbb C^3\) ⋮ Restricted Gröbner fans and re-embeddings of affine algebras ⋮ Exotic embeddings of open subsets of affine space ⋮ Exotic embeddings of smooth affine varieties ⋮ Simple birational extensions of the polynomial algebra ℂ^{[3}] ⋮ Non-extendable isomorphisms between affine varieties

Cites Work

• On the hypersurface \(x+x^2y+z^2+t^3=0\) in \(\mathbb{C}^4\) or a \(\mathbb{C}^3\)-like threefold which is not \(\mathbb{C}^3\)
• The extension of regular and rational embeddings
• On finding and cancelling variables in k[X,Y,Z]
• Affine modifications and affine hypersurfaces with a very transitive automorphism group
• Smooth contractible hypersurfaces in \(\mathbb{C}^ n\) and exotic algebraic structures on \(\mathbb{C}^ 3\)
• A hypersurface which has the Abhyankar-Moh property
• Propriétés topologiques des polynômes de deux variables complexes et automorphismes algébriques de l'espace \(C^2\)
• On the embedding dimension of an affine variety
• Extensions of Isomorphisms between Affine Algebraic Subvarieties of k n Automorphisms of k n
• On Linear Planes
• On exotic algebraic structures on affine spaces
• Subvarieties of Cn with non-extendable autormorphisms
• Uniqueness of plane embeddings of special curves
• Knots
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