The period-index problem for hyper-Kähler varieties via hyperholomorphic bundles
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908415459065856 |
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| author | Hotchkiss, James Maulik, Davesh Shen, Junliang Yin, Qizheng Zhang, Ruxuan |
| author_facet | Hotchkiss, James Maulik, Davesh Shen, Junliang Yin, Qizheng Zhang, Ruxuan |
| contents | We prove new bounds for the period-index problem for hyper-Kähler varieties of $K3^{[n]}$-type using projectively hyperholomorphic bundles constructed by Markman. We show that $\mathrm{dim}(X)$ is a bound for any $X$ of $K3^{[n]}$-type. We also show that $\frac{1}{2}\mathrm{dim}(X)$ is a bound for most Brauer classes when the Picard rank of $X$ is at least two, providing evidence for a conjecture of Huybrechts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The period-index problem for hyper-Kähler varieties via hyperholomorphic bundles Hotchkiss, James Maulik, Davesh Shen, Junliang Yin, Qizheng Zhang, Ruxuan Algebraic Geometry We prove new bounds for the period-index problem for hyper-Kähler varieties of $K3^{[n]}$-type using projectively hyperholomorphic bundles constructed by Markman. We show that $\mathrm{dim}(X)$ is a bound for any $X$ of $K3^{[n]}$-type. We also show that $\frac{1}{2}\mathrm{dim}(X)$ is a bound for most Brauer classes when the Picard rank of $X$ is at least two, providing evidence for a conjecture of Huybrechts. |
| title | The period-index problem for hyper-Kähler varieties via hyperholomorphic bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.09774 |