The numerical Amitsur group
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914117292392448 |
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| author | Duncan, Alexander Sharma, Shreya |
| author_facet | Duncan, Alexander Sharma, Shreya |
| contents | The Amitsur subgroup of a variety with a group action measures the failure of the action to lift to the total spaces of its line bundles. We introduce the "numerical Amitsur group," which is an approximation of the ordinary Amitsur subgroup that can be computed using only the Euler-Poincaré characteristic on the Picard group. As an application, we find a uniform upper bound on the exponent of the Amitsur subgroup that depends only on the dimension and arithmetic genus of the variety and is independent of the group. Finally, we compute Amitsur subgroups of toric varieties using these ideas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The numerical Amitsur group Duncan, Alexander Sharma, Shreya Algebraic Geometry 14L30 (Primary), 14E07 (Secondary) The Amitsur subgroup of a variety with a group action measures the failure of the action to lift to the total spaces of its line bundles. We introduce the "numerical Amitsur group," which is an approximation of the ordinary Amitsur subgroup that can be computed using only the Euler-Poincaré characteristic on the Picard group. As an application, we find a uniform upper bound on the exponent of the Amitsur subgroup that depends only on the dimension and arithmetic genus of the variety and is independent of the group. Finally, we compute Amitsur subgroups of toric varieties using these ideas. |
| title | The numerical Amitsur group |
| topic | Algebraic Geometry 14L30 (Primary), 14E07 (Secondary) |
| url | https://arxiv.org/abs/2505.23957 |