Configurations of points on a line up to scaling or translation
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913201063460864 |
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| author | Zahariuc, Adrian |
| author_facet | Zahariuc, Adrian |
| contents | We prove that the Losev--Manin compactification of the space of configurations of $n$ points on ${\mathbb P}^1 \backslash \{0,\infty\}$ modulo scaling degenerates (isotrivially) to a compactification of the space of configurations of $n$ points on ${\mathbb A}^1$ modulo translation. The latter resembles the compactification constructed by Ziltener and Mau--Woodward, but allows the marked points to coincide, making it a ${\mathbb G}_a^{n-1}$-variety, which mirrors the fact that the Losev--Manin space is toric. The degeneration is compatible with the actions of ${\mathbb G}_m^{n-1}$ and ${\mathbb G}_a^{n-1}$ in the sense that these actions fit together globally in the total space of the degeneration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_11357 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Configurations of points on a line up to scaling or translation Zahariuc, Adrian Algebraic Geometry 14H10, 14M27, 14L30 We prove that the Losev--Manin compactification of the space of configurations of $n$ points on ${\mathbb P}^1 \backslash \{0,\infty\}$ modulo scaling degenerates (isotrivially) to a compactification of the space of configurations of $n$ points on ${\mathbb A}^1$ modulo translation. The latter resembles the compactification constructed by Ziltener and Mau--Woodward, but allows the marked points to coincide, making it a ${\mathbb G}_a^{n-1}$-variety, which mirrors the fact that the Losev--Manin space is toric. The degeneration is compatible with the actions of ${\mathbb G}_m^{n-1}$ and ${\mathbb G}_a^{n-1}$ in the sense that these actions fit together globally in the total space of the degeneration. |
| title | Configurations of points on a line up to scaling or translation |
| topic | Algebraic Geometry 14H10, 14M27, 14L30 |
| url | https://arxiv.org/abs/2102.11357 |