Automorphisms of generalised Kummer fourfolds
arXiv:1512.00225
Abstract
We classify non symplectic prime order automorphisms and all finite order symplectic automorphism groups of generalised Kummer fourfolds using lattice theory and recent results on ample cones and monodromy groups. We study various geometric realisations of the automorphisms obtained in the classification. In the case of higher dimensional generalised Kummers, we provide full results for finite symplectic automorphisms groups and we sketch the classification for prime order non-symplectic groups.
arXiv commentv2: corrected some typos
References in corpus (8)
- A survey of Torelli and monodromy results for holomorphic-symplectic varieties
- Bridgeland's stability and the positive cone of the moduli spaces of stable objects on an abelian surface
- Classification of automorphisms on a deformation family of hyperkähler fourfolds by p-elementary lattices
- The 290 fixed-point sublattices of the Leech lattice
- On natural deformations of symplectic automorphisms of manifolds of K3^[n] type
- No cohomologically trivial non-trivial automorphism of generalized Kummer manifolds
- Non-natural non-symplectic involutions on symplectic manifolds of K3^{[2]}-type
- Prime order automorphisms of abelian surfaces: a lattice-theoretic point of view