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

Author:

Lisa Marquand, Stevell Muller

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Number Theory (math.NT)

journal:

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date:

2023-10-09 16:00:00

Abstract

We classify finite groups that act faithfully by symplectic birational transformations on an irreducible holomorphic symplectic (IHS) manifold of $OG10$ type. In particular, up to deformation there are 379 birational conjugacy classes of pairs $(X,G)$, consisting of an IHS manifold $X$ of $OG10$ type and a saturated, finite subgroup $G\leq \mathrm{Bir}_s(X)$. We determine the action of $G$ on $H^2(X,\mathbb{Z})$ for each case. 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.