Classification of automorphisms on a deformation family of hyperkähler fourfolds by p-elementary lattices

Abstract

We give a classification of all non-symplectic automorphisms of prime order p acting on irreducible holomorphic symplectic fourfolds deformation equivalent to the Hilbert scheme of two points on a K3 surface, for p=2,3 and 7\leq p \leq 19. Our classification relates the isometry classes of two natural lattices associated to the action of the automorphism on the second cohomology group with integer coefficients with some invariants of the fixed locus and we provide explicit examples. As an application, we find new examples of non-natural non-symplectic automorphisms.

References in corpus (11)

• A survey of Torelli and monodromy results for holomorphic-symplectic varieties
• A global Torelli theorem for hyperkahler manifolds
• Antisymplectic involutions of holomorphic symplectic manifolds
• Automorphisms of prime order of smooth cubic n-folds
• Symplectic involutions of holomorphic symplectic fourfolds
• Smith theory and irreducible holomorphic symplectic manifolds
• Symplectic involutions on deformations of K3^[2]
• Non-symplectic involutions of irreducible symplectic manifolds of K3^[n]-type
• Non-natural non-symplectic involutions on symplectic manifolds of K3^{[2]}-type
• Lattice polarized irreducible holomorphic symplectic manifolds
• A Complex Ball Uniformization of the Moduli Space of Cubic Surfaces Via Periods of K3 Surfaces

Cited by in corpus (15)

• Induced Automorphisms on Irreducible Symplectic Manifolds
• Hyperkähler fourfolds and Kummer surfaces
• Moduli Spaces of Symmetric Cubic Fourfolds and Locally Symmetric Varieties
• Complex ball quotients from manifolds of $K{3}^{[n]}$-type
• Symplectic birational transformations of finite order on O'Grady's sixfolds
• Automorphisms and Periods of Cubic Fourfolds
• Towards a classification of symplectic automorphisms on manifolds of $K{3}^{[n]}$ type
• On the nonsymplectic involutions of the Hilbert square of a K3 surface
• Symplectic involutions of $K{3}^{[n]}$ type and Kummer $n$ type manifolds
• Automorphisms of generalised Kummer fourfolds
• Brane involutions on irreducible holomorphic symplectic manifolds
• Automorphism groups of smooth cubic threefolds
• Integral cohomology of the Generalized Kummer fourfold
• Isometries of ideal lattices and hyperkähler manifolds
• Index of coregularity zero log Calabi-Yau pairs