Hensel lifting algorithms for quadratic forms

Brandhorst, Simon; Veniani, Davide

doi:10.1090/mcom/3909

Math. Comp.

2023

DOI: 10.1090/mcom/3909

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Hensel lifting algorithms for quadratic forms

Simon Brandhorst,

Davide Veniani

Abstract: We provide an algorithm to compute generators of the orthogonal group of the discriminant group associated to an integral quadratic lattice over the integers. We give a closed formula for its order.

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Finite subgroups of automorphisms of K3 surfaces

Brandhorst

Hofmann

2023

Forum of Mathematics, Sigma

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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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Finite subgroups of automorphisms of K3 surfaces

Brandhorst

Hofmann

2023

Forum of Mathematics, Sigma

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show abstract

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Hensel lifting algorithms for quadratic forms

Abstract: We provide an algorithm to compute generators of the orthogonal group of the discriminant group associated to an integral quadratic lattice over the integers. We give a closed formula for its order.

Cited by 1 publication

References 10 publications

Finite subgroups of automorphisms of K3 surfaces

Finite subgroups of automorphisms of K3 surfaces

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