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

2022/10/24 by Yuta Takada, Takada, Yuta · 1 citation
Mathematics · #11H56 #14J28 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2210.12946

openalex publication_date 2022/10/24 · openalex created_date 2022/10/31 · openalex updated_date 2026/07/28

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.

Cited by

• Non-projective K3 surfaces with real or Salem multiplication

Related

• Automorphisms of K3 surfaces, signatures, and isometries of lattices
• Isometries of lattices and automorphisms of K3 surfaces
• The third smallest Salem number in automorphisms of K3 surfaces
• Characteristic polynomials of isometries of even unimodular lattices
• Automorphisms of elliptic K3 surfaces and Salem numbers of maximal degree