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

摘要

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 Boissiere, Cattaneo, Nieper-Wisskirchen, and Sarti.