A note on the Nielsen realization problem for hyper-Kähler manifolds

Abstract

We give an answer to the Nielsen realization problem for hyper-Kähler manifolds in terms of the same invariant used for K3 surfaces. We determine that, for some of the known deformation types, the representation of the mapping class group on the second cohomology admits a section on its image.

Removed section 2 and other minor changes, 7 pages. Comments are welcome!