Limit points and additive group actions
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866911799400464384 |
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| author | Arzhantsev, Ivan |
| author_facet | Arzhantsev, Ivan |
| contents | We show that an effective action of the one-dimensional torus $\mathbb{G}_m$ on a normal affine algebraic variety $X$ can be extended to an effective action of a semi-direct product $\mathbb{G}_m\rightthreetimes\mathbb{G}_a$ with the same general orbit closures if and only if there is a divisor $D$ on $X$ that consists of $\mathbb{G}_m$-fixed points. This result is applied to the study of orbits of the automorphism group $\text{Aut}(X)$ on $X$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2102_11330 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Limit points and additive group actions Arzhantsev, Ivan Algebraic Geometry Commutative Algebra Primary 14J50, 14R20, Secondary 13A50, 14L30 We show that an effective action of the one-dimensional torus $\mathbb{G}_m$ on a normal affine algebraic variety $X$ can be extended to an effective action of a semi-direct product $\mathbb{G}_m\rightthreetimes\mathbb{G}_a$ with the same general orbit closures if and only if there is a divisor $D$ on $X$ that consists of $\mathbb{G}_m$-fixed points. This result is applied to the study of orbits of the automorphism group $\text{Aut}(X)$ on $X$. |
| title | Limit points and additive group actions |
| topic | Algebraic Geometry Commutative Algebra Primary 14J50, 14R20, Secondary 13A50, 14L30 |
| url | https://arxiv.org/abs/2102.11330 |