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arXiv · 1210.2050

Chow's Theorem for Linear Spaces

Hans Havlicek
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Abstract

If $\phi: L\to L'$ is a bijection from the set of lines of a linear space $(P,L)$ onto the set of lines of a linear space $(P',L')$ ($\dim P, \dim P'\geq 3$), such that intersecting lines go over to intersecting lines in both directions, then $\phi$ is arising from a collineation of $(P,L)$ onto $(P',L')$ or a collineation of $(P,L)$ onto the dual linear space of $(P',L')$. However, the second possibility can only occur when $(P,L)$ and $(P',L')$ are 3-dimensional generalized projective spaces.

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Hans Havlicek. 2012-10-07. Chow's Theorem for Linear Spaces. https://doi.org/10.1016/s0012-365x(99)00080-1

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