A Characteristic Property of Elliptic Plücker Transformations
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arXiv
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| Format: | Preprint |
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2012
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| _version_ | 1866913229782908928 |
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| author | Havlicek, Hans |
| author_facet | Havlicek, Hans |
| contents | We discuss elliptic Plücker transformations of three-dimensional elliptic spaces. These are permutations on the set of lines such that any two related (orthogonally intersecting or identical) lines go over to related lines in both directions. It will be shown that for "classical" elliptic 3-spaces a bijection of its lines is already a Plücker transformation, if related lines go over to related lines. Moreover, if the ground field admits only surjective monomorphisms, then "bijection" can be replaced by "injection". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1210_1962 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | A Characteristic Property of Elliptic Plücker Transformations Havlicek, Hans Algebraic Geometry 51F20 We discuss elliptic Plücker transformations of three-dimensional elliptic spaces. These are permutations on the set of lines such that any two related (orthogonally intersecting or identical) lines go over to related lines in both directions. It will be shown that for "classical" elliptic 3-spaces a bijection of its lines is already a Plücker transformation, if related lines go over to related lines. Moreover, if the ground field admits only surjective monomorphisms, then "bijection" can be replaced by "injection". |
| title | A Characteristic Property of Elliptic Plücker Transformations |
| topic | Algebraic Geometry 51F20 |
| url | https://arxiv.org/abs/1210.1962 |