The period-index problem for hyper-Kähler varieties via hyperholomorphic bundles Article Swipe
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James Hotchkiss
,
Davesh Maulik
,
Junliang Shen
,
Qizheng Yin
,
Ruxuan Zhang
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.09774
· OA: W4407632227
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.09774
· OA: W4407632227
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.
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