The hyperkähler period-index conjecture is false

Abstract

Huybrechts conjectured that for every Brauer class $\alpha$ on a hyperkähler variety $X$ we have that $\mathrm{ind}(\alpha )\mid \mathrm{per}(\alpha {)}^{\dim (X)/2}$, strengthening the usual period-index conjecture. We show that this fails on certain hyperkähler fourfolds, both in type $\mathrm{K}{3}^{[2]}$ and ${\mathrm{Kum}}^2$.

arXiv comment11 pages, all comments welcome