The period-index problem for hyperkähler varieties: Lower and upper bounds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912770726821888 |
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| author | Bottini, Alessio Huybrechts, Daniel |
| author_facet | Bottini, Alessio Huybrechts, Daniel |
| contents | It is expected that a stronger form of the period-index conjecture holds for hyperkähler varieties. Following ideas of Hotchkiss, we provide further evidence for this expectation by proving a version in which the index is replaced by the Hodge-theoretic index. We also show that the hyperkähler period-index conjecture is optimal. As an application, we prove that Mumford-Tate general hyperkähler varieties cannot be covered by families of elliptic curves passing through a fixed point. By extending work of Hotchkiss, Maulik, Shen, Yin, and Zhang, we prove the hyperkähler period-index conjecture for non-special coprime Brauer class on hyperkähler varieties of K3^n-type without any restriction on the Picard number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15131 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The period-index problem for hyperkähler varieties: Lower and upper bounds Bottini, Alessio Huybrechts, Daniel Algebraic Geometry It is expected that a stronger form of the period-index conjecture holds for hyperkähler varieties. Following ideas of Hotchkiss, we provide further evidence for this expectation by proving a version in which the index is replaced by the Hodge-theoretic index. We also show that the hyperkähler period-index conjecture is optimal. As an application, we prove that Mumford-Tate general hyperkähler varieties cannot be covered by families of elliptic curves passing through a fixed point. By extending work of Hotchkiss, Maulik, Shen, Yin, and Zhang, we prove the hyperkähler period-index conjecture for non-special coprime Brauer class on hyperkähler varieties of K3^n-type without any restriction on the Picard number. |
| title | The period-index problem for hyperkähler varieties: Lower and upper bounds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.15131 |