On conjugacy of additive actions in the affine Cremona group
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914948919066624 |
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| author | Arzhantsev, Ivan |
| author_facet | Arzhantsev, Ivan |
| contents | An additive action on an irreducible algebraic variety $X$ is an effective action $\mathbb{G}_a^n\times X\to X$ with an open orbit of the vector group $\mathbb{G}_a^n$. Any two additive actions on $X$ are conjugate by a birational automorphism of $X$. We prove that, if $X$ is the projective space, the conjugating element can be chosen in the affine Cremona group and it is given by so-called basic polynomials of the corresponding local algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12096 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On conjugacy of additive actions in the affine Cremona group Arzhantsev, Ivan Algebraic Geometry Primary 14L30, 14R10, Secondary 13E10, 14E07, 14J50 An additive action on an irreducible algebraic variety $X$ is an effective action $\mathbb{G}_a^n\times X\to X$ with an open orbit of the vector group $\mathbb{G}_a^n$. Any two additive actions on $X$ are conjugate by a birational automorphism of $X$. We prove that, if $X$ is the projective space, the conjugating element can be chosen in the affine Cremona group and it is given by so-called basic polynomials of the corresponding local algebra. |
| title | On conjugacy of additive actions in the affine Cremona group |
| topic | Algebraic Geometry Primary 14L30, 14R10, Secondary 13E10, 14E07, 14J50 |
| url | https://arxiv.org/abs/2308.12096 |