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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0409472-6
PII: S 0002-9939(1976)0409472-6
Keywords: Biregular hyperplane, generic hyperplane, embedded hyperplane, epimorphisms of polynomial rings, automorphisms of polynomial rings
Article copyright: © Copyright 1976 American Mathematical Society