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

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.

Final version, accepted for publication in Forum Math., Sigma. Few improvements and typos corrected. 43 pages, 4 appendices, 3 tables + 2 tables in ancillary files. Tables 4 and 5 as well as computational data and some notebooks are included in a Zenodo database