Finite Symplectic Automorphisms of Hyperkähler Manifolds of $K3^{[n]}$-Type Act Trivially on Discriminant Groups
Year: 2026
Type: preprint
Abstract: We give an alternative proof of Mongardi's result that every finite group of symplectic automorphisms of a hyperkähler manifold of $K3^{[n]}$-type acts trivially on the discriminant groups of its second cohomology lattice and its coinvariant lattice. The proof combines sphere-packing bounds, Vinberg's reflection chambers and structure results on even $2$-elementary lattices.
Source: arXiv (Cornell University)
Authors: Fu, Jie, Wang, Shihao, Zheng, Zhiwei
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224077179