Lattice isometries and K3 surface automorphisms: Salem numbers of degree 20

TL;DR

This paper extends a theorem on lattice isometries to include determinant -1 cases and demonstrates that all Salem numbers of degree 20 can be realized as automorphism entropies of nonprojective K3 surfaces.

Contribution

It generalizes Bayer-Fluckiger's theorem to isometries with determinant -1 and links Salem numbers of degree 20 to K3 surface automorphisms.

Findings

Logarithm of every Salem number of degree 20 is a topological entropy of a K3 automorphism.

Extended theorem applies to isometries with determinant -1.

Established a connection between Salem numbers and K3 surface automorphisms.

Abstract

This article extends Bayer-Fluckiger's theorem on characteristic polynomials of isometries on an even unimodular lattice to the case where the isometries have determinant $-1$. As an application, we show that the logarithm of every Salem number of degree $20$ is realized as the topological entropy of an automorphism of a nonprojective K3 surface.