Symplectic involutions of K3[n]$K3^{[n]}$ type and Kummer n$n$ type manifolds.

In this paper, we describe the fixed locus of a symplectic involution on a hyper‐Kähler manifold of type K3[n]$K3^{[n]}$ or of Kummer n$n$ type. We prove that the fixed locus consists of finitely many copies of deformations of Hilbert schemes of K3$K3$ surfaces of lower dimensions and isolated fixed points. [ABSTRACT FROM AUTHOR]