Work

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

Year: 2025

Type: article

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

Source: Forum of Mathematics Sigma

DOI: 10.1017/fms.2025.10077

Authors: Lisa Marquand, Stevell Muller

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,650

Funder: Deutsche Forschungsgemeinschaft

Award: TRR 195: Symbolische Werkzeuge in der Mathematik und ihre Anwendung