Chow's Theorem for Linear Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2012
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| _version_ | 1866909100579749888 |
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| author | Havlicek, Hans |
| author_facet | Havlicek, Hans |
| contents | If $ϕ: L\to L'$ 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 $ϕ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1210_2050 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Chow's Theorem for Linear Spaces Havlicek, Hans Algebraic Geometry 51A10 If $ϕ: L\to L'$ 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 $ϕ$ 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. |
| title | Chow's Theorem for Linear Spaces |
| topic | Algebraic Geometry 51A10 |
| url | https://arxiv.org/abs/1210.2050 |