On linear planes
Author: Avinash Sathaye
Journal: Proc. Amer. Math. Soc. 56 (1976), 1-7
MSC: Primary 14E25; Secondary 13B15, 14E35
MathSciNet review: 0409472
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Abstract: A linear plane over a ground field $k$ is an algebraic surface in affine $3$-space over $k$ which is biregular to the affine plane and whose equation is linear in one of the three variables of the $3$-space. In this note we give a concrete description of a linear plane over a field of characteristic zero, thereby proving it to be an embedded plane, i.e. we show that by an automorphism of the affine $3$-space, it can be transformed to a coordinate plane.
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- Shreeram S. Abhyankar and Tzuong Tsieng Moh, Embeddings of the line in the plane, J. Reine Angew. Math. 276 (1975), 148–166. MR 379502
- Peter Russell, Simple birational extensions of two dimensional affine rational domains, Compositio Math. 33 (1976), no. 2, 197–208. MR 429935
Shreeram S. Abhyankar, William Heinzer and Paul Eakin, On the uniqueness of the coefficient ring in a polynomial ring, J. Algebra 23 (1972). 310-342. MR 46 #5300.
Shreeram S. Abhyankar and Tzuong-tsieng Moh, Embeddings of the line in the plane, J. Reine Angew. Math. (to appear).
Peter Russell, Simple birational extension of two dimensional affine rational domains (to appear).
Keywords: Biregular hyperplane, generic hyperplane, embedded hyperplane, epimorphisms of polynomial rings, automorphisms of polynomial rings
Article copyright: © Copyright 1976 American Mathematical Society