TL;DR
This paper introduces a family of homogeneous hypersurfaces in affine space that generalize the classical Cayley surface, providing a new perspective on affine geometry across various dimensions.
Contribution
It constructs a new family of hypersurfaces in affine space that extend the properties of the Cayley surface to higher dimensions.
Findings
Provides explicit equations for the hypersurfaces.
Shows the hypersurfaces are homogeneous in affine space.
Generalizes the Cayley surface to all dimensions.
Abstract
We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, generalising the Cayley surface.
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