Automorphisms of even unimodular lattices and unramified Salem numbers
type: Item
instance of: scholarly article
title: Automorphisms of even unimodular lattices and unramified Salem numbers
zbMATH Open document ID: 1022.11016
DOI: 10.1016/S0021-8693(02)00552-5
author: Curtis T. McMullen
author: Benedict H. Gross
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: The authors study the characteristic polynomials of automorphisms of even, indefinite, unimodular lattices with signature \((p,q)\). It is well known that such lattices exist if and only if \(p\equiv 0 \bmod 8\) and that they are unique up to isomorphism. The authors are interested in the question of which monic polynomials arise in this way. In particular they show that this is the case for any Salem polynomial \(S(x)\) of degree \(2n=p+q\) satisfying \(S(-1)S(1)= (-1)^n\). The authors apply their results in the case of the lattice \(H^2(X,\mathbb{Z})\) of a complex \(K3\) surface \(X\). They show the existence of such surfaces \(X\) and automorphisms \(f:X\to X\) such that the corresponding characteristic polynomial is equal to a given Salem polynomial \(S(X)\) of degree 22 with \(S(-1)S(1)=-1\).
Mathematics Subject Classification ID: 11E12
zbMATH DE Number: 1868065
zbMATH Keywords: characteristic polynomials of automorphisms
zbMATH Keywords: even unimodular lattices
zbMATH Keywords: monic polynomials
zbMATH Keywords: Salem polynomial
zbMATH Keywords: complex K3 surface
reviewed by: Helmut Koch
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1868065