Finite groups of symplectic birational transformations of IHS manifolds of $OG10$ type

TL;DR

This paper classifies finite groups acting symplectically on OG10 type IHS manifolds, linking their actions to isometry groups and automorphisms of cubic fourfolds, with results supported by computational methods.

Contribution

It provides the first classification of finite symplectic birational groups on OG10 IHS manifolds, connecting group actions to cubic fourfold automorphisms.

Findings

Finite groups acting symplectically are conjugate to subgroups of 375 isometry groups.

A criterion relates these groups to automorphisms of cubic fourfolds.

Results are supported by computational analysis and are publicly available.

Abstract

We classify finite groups that act faithfully by symplectic birational transformations on an irreducible holomorphic symplectic (IHS) manifold of OG10 type. In particular, if X is an IHS manifold of OG10 type and G a finite subgroup of symplectic birational transformations of X, then the action of G on H2(X, Z) is conjugate to a subgroup of one of 375 groups of isometries. We prove a criterion for when such a group is determined by a group of automorphisms acting on a cubic fourfold, and apply it to our classification. Our proof is computer aided and our results are available in a Zenodo dataset.