Symplectic involutions on deformations of K3^[2]

Abstract

Let X be a Hyperkähler variety deformation equivalent to the Hilbert square on a K3 surface and let f be an involution preserving the symplectic form. We prove that the fixed locus of f consists of 28 isolated points and 1 K3 surface, moreover the anti-invariant lattice of the induced involution on H^2(X,Z) is isomorphic to E_8(-2). Finally we prove that any couple consisting of one such variety and a symplectic involution on it can be deformed into a couple consisting of the Hilbert square of a K3 surface and the involution induced by a Nikulin involution on the K3 surface.

Final version, to appear on Central European Journal of Mathematics

References in corpus (2)

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

Cited by in corpus (7)

• Classification of automorphisms on a deformation family of hyperkähler fourfolds by p-elementary lattices
• On natural deformations of symplectic automorphisms of manifolds of K3^[n] type
• Moduli Spaces of Symmetric Cubic Fourfolds and Locally Symmetric Varieties
• Symplectic birational transformations of finite order on O'Grady's sixfolds
• Symplectic involutions of $K{3}^{[n]}$ type and Kummer $n$ type manifolds
• Brane involutions on irreducible holomorphic symplectic manifolds
• Projective models of Nikulin orbifolds