Geodesic
Finite subgroups of automorphisms of K3 surfaces
Forum of Mathematics, Sigma, Tome 11 (2023)

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We give a complete classification of finite subgroups of automorphisms of K3 surfaces up to deformation. The classification is in terms of Hodge theoretic data associated to certain conjugacy classes of finite subgroups of the orthogonal group of the K3 lattice. The moduli theory of K3 surfaces, in particular the surjectivity of the period map and the strong Torelli theorem allow us to interpret this datum geometrically. Our approach is computer aided and involves Hermitian lattices over number fields. 
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     author = {Simon Brandhorst and Tommy Hofmann},
     title = {Finite subgroups of automorphisms of {K3} surfaces},
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Simon Brandhorst; Tommy Hofmann. Finite subgroups of automorphisms of K3 surfaces. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.50

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