1976•Proceedings of the American Mathematical SocietyRequires access
On Linear Planes
Avinash Madhav Sathaye
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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.