Finite groups of symplectic birational transformations of IHS manifolds of $\mathit {OG10}$ type

Marquand, Lisa  ; Muller, Stevell 

Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e117

Résumé

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 $H^2(X,\mathbb {Z})$ 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.

Détail

DOI : 10.1017/fms.2025.10077

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