Finite groupoids of configurations of lines in $\mathbb{P}^{3}_{\mathbb{C}}$
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909893297963008 |
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| author | Kettinger, Jake |
| author_facet | Kettinger, Jake |
| contents | In this paper, we investigate groupoids coming from configurations of lines in three-dimensional space. Given a point and two skew lines in $\mathbb{P}^{3}_{K}$ over a field $K$, there exists a unique line containing the given point and meeting the two given lines. We use this construction to define a projection function from one line to another by using a skew line as an auxiliary. This way, we may create a groupoid whose objects are lines in a configuration, and whose morphisms are induced by these projection functions. We look at specific configurations for $K=\mathbb{C}$ that yield groupoids with finite automorphism groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite groupoids of configurations of lines in $\mathbb{P}^{3}_{\mathbb{C}}$ Kettinger, Jake Algebraic Geometry Group Theory In this paper, we investigate groupoids coming from configurations of lines in three-dimensional space. Given a point and two skew lines in $\mathbb{P}^{3}_{K}$ over a field $K$, there exists a unique line containing the given point and meeting the two given lines. We use this construction to define a projection function from one line to another by using a skew line as an auxiliary. This way, we may create a groupoid whose objects are lines in a configuration, and whose morphisms are induced by these projection functions. We look at specific configurations for $K=\mathbb{C}$ that yield groupoids with finite automorphism groups. |
| title | Finite groupoids of configurations of lines in $\mathbb{P}^{3}_{\mathbb{C}}$ |
| topic | Algebraic Geometry Group Theory |
| url | https://arxiv.org/abs/2511.05454 |