On the characterization of affine toric varieties by their automorphism group
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929325838696448 |
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| author | Díaz, Roberto Liendo, Alvaro Regeta, Andriy |
| author_facet | Díaz, Roberto Liendo, Alvaro Regeta, Andriy |
| contents | In this paper we show that a normal affine toric variety X different from the algebraic torus is uniquely determined by its automorphism group in the category of affine irreducible, not necessarily normal, algebraic varieties if and only if X is isomorphic to the product of the affine line and another affine toric variety. In the case where X is the algebraic torus T, we reach the same conclusion if we restrict the category to only include irreducible varieties of dimension at most the dimension of T. There are examples of varieties of dimension one higher than T having the same automorphism group of T. Hence, this last result is optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08040 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the characterization of affine toric varieties by their automorphism group Díaz, Roberto Liendo, Alvaro Regeta, Andriy Algebraic Geometry 14R20, 14M25 In this paper we show that a normal affine toric variety X different from the algebraic torus is uniquely determined by its automorphism group in the category of affine irreducible, not necessarily normal, algebraic varieties if and only if X is isomorphic to the product of the affine line and another affine toric variety. In the case where X is the algebraic torus T, we reach the same conclusion if we restrict the category to only include irreducible varieties of dimension at most the dimension of T. There are examples of varieties of dimension one higher than T having the same automorphism group of T. Hence, this last result is optimal. |
| title | On the characterization of affine toric varieties by their automorphism group |
| topic | Algebraic Geometry 14R20, 14M25 |
| url | https://arxiv.org/abs/2308.08040 |