Moduli Spaces of Cubic Threefolds and of Irreducible Holomorphic Symplectic Manifolds

Abstract

We extend the lattice-theoretic approach of Brandhorst-Cattaneo to classify algebraically trivial actions on the known IHS manifolds, up to deformation and birational conjugacy. In particular, we classify even order algebraically trivial non symplectic automorphisms, with or without trivial discriminant action. In the case of nontrivial discriminant actions, we show that such automorphisms exist only for finitely many known deformation types and orders.