On the nonsymplectic involutions of the Hilbert square of a K3 surface

Abstract

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 nonsymplectic involution with invariant lattice of rank one. In particular we geometrically describe some new involutions of the Hilbert square of a K3 surface, whose existence was proven in a previous work of Boissiere, Cattaneo, Nieper-Wisskirchen and Sarti.

References in corpus (7)

• A survey of Torelli and monodromy results for holomorphic-symplectic varieties
• Moduli spaces of irreducible symplectic manifolds
• Classification of automorphisms on a deformation family of hyperkähler fourfolds by p-elementary lattices
• Antisymplectic involutions of holomorphic symplectic manifolds
• Integral constraints on the monodromy group of the hyperkahler resolution of a symmetric product of a K3 surface
• On natural deformations of symplectic automorphisms of manifolds of K3^[n] type
• Non-symplectic involutions of irreducible symplectic manifolds of K3^[n]-type