Finite subgroups of automorphisms of K3 surfaces

被引：2

作者：

Brandhorst, Simon ^{[1
]}

Hofmann, Tommy ^{[2
]}

机构：

[1] Univ Saarland, Fak Math & Informat, Campus E2-4, D-66123 Saarbrucken, Germany

[2] Univ Siegen, Nat Wissensch Tech Fak, Walter Flex Str 3, D-57076 Siegen, Germany

来源：

FORUM OF MATHEMATICS SIGMA | 2023年 / 11卷

关键词：

14J28; 14J50; 11E39; 11H56; NON-SYMPLECTIC AUTOMORPHISMS; INTEGRAL-REPRESENTATIONS; HERMITIAN-FORMS; ORDER; CLASSIFICATION; EMBEDDINGS; ISOMETRIES; LATTICES; NUMBER;

D O I：

10.1017/fms.2023.50

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：57

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