On the non-symplectic involutions of the Hilbert square of a K3 surface

We investigate the interplay between the moduli spaces of ample (2)-polarized IHS manifolds of type K3[2] and of IHS manifolds of type K3[2] with a non-symplectic involution with invariant lattice of rank one. In particular, we describe geometrically some new involutions of the Hilbert square of a K3 surface whose existence was proven in a previous paper of Boissière, Cattaneo, Nieper-Wisskirchen, and Sarti