On linear planes
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- by Avinash Sathaye PDF
- Proc. Amer. Math. Soc. 56 (1976), 1-7 Request permission
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.References
- 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 306173, DOI 10.1016/0021-8693(72)90134-2
- 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
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 1-7
- MSC: Primary 14E25; Secondary 13B15, 14E35
- DOI: https://doi.org/10.1090/S0002-9939-1976-0409472-6
- MathSciNet review: 0409472