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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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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