Symplectic birational transformations of finite order on O’Grady’s sixfolds

Abstract

We prove that any symplectic automorphism of finite order on a manifold of type $\mathrm{OG}6$ acts trivially on the Beauville–Bogomolov–Fujiki lattice and that any birational transformation of finite order acts trivially on its discriminant group. Moreover, we classify all possible invariant and coinvariant sublattices.