Non-natural non-symplectic involutions on symplectic manifolds of K3^{[2]}-type

Abstract

We study non-symplectic involutions on irreducible symplectic manifolds of K3^{[2]}-type with 19 parameters, which is the second largest possible. We classify the conjugacy classes of cohomological representations into four different types and show that there are at most five deformation types, two of which are given by natural involutions and their flops. Next, we give a geometric realisation of one of the new types using moduli spaces of sheaves on K3 surfaces. The geometry of the manifold and the new involution is described in detail.

22 pages

References in corpus (3)

• A survey of Torelli and monodromy results for holomorphic-symplectic varieties
• A global Torelli theorem for hyperkahler manifolds
• Antisymplectic involutions of holomorphic symplectic manifolds

Cited by in corpus (6)

• Classification of automorphisms on a deformation family of hyperkähler fourfolds by p-elementary lattices
• Induced Automorphisms on Irreducible Symplectic Manifolds
• Induced birational transformations on O'Grady's sixfolds
• Automorphisms of generalised Kummer fourfolds
• Non-symplectic automorphisms of odd prime order on manifolds of $K{3}^{[n]}$-type
• Isometries of ideal lattices and hyperkähler manifolds