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

TL;DR

This paper proves that finite order symplectic automorphisms and birational transformations on OG6 manifolds act trivially on key lattice structures, and it classifies their invariant sublattices.

Contribution

It establishes trivial action of finite order automorphisms on lattice structures and provides a classification of invariant sublattices for OG6 manifolds.

Findings

Finite order symplectic automorphisms act trivially on the Beauville--Bogomolov--Fujiki lattice.

Finite order birational transformations act trivially on the discriminant group.

Complete classification of invariant and coinvariant sublattices for OG6 manifolds.

Abstract

We prove that any symplectic automorphism of finite order on a manifold of type OG6 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.