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arXiv · 2502.09774

The period-index problem for hyper-K\"ahler varieties via hyperholomorphic bundles

James Hotchkiss·Davesh Maulik·Junliang Shen·Qizheng Yin·Ruxuan Zhang
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Abstract

We prove new bounds for the period-index problem for hyper-K\"ahler 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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James Hotchkiss, Davesh Maulik, Junliang Shen, Qizheng Yin, Ruxuan Zhang. 2025-02-13. The period-index problem for hyper-K\"ahler varieties via hyperholomorphic bundles. https://arxiv.org/abs/2502.09774

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