The period-index problem for hyper-Kähler varieties via hyperholomorphic bundles

Abstract

We prove new bounds for the period-index problem for hyper-Kähler varieties of $K{3}^{[n]}$-type using projectively hyperholomorphic bundles constructed by Markman. We show that $\dim (X)$ is a bound for any $X$ of $K{3}^{[n]}$-type. We also show that $\frac{1}{2}\dim (X)$ is a bound for most Brauer classes when the Picard rank of $X$ is at least two, providing evidence for a conjecture of Huybrechts.

20 pages. Revised version with corrections