K3 surfaces with non-symplectic automorphisms of 2-power order

TL;DR

This paper classifies certain K3 surfaces with non-symplectic automorphisms of 2-power order, linking automorphism order to the transcendental lattice rank, and explores their arithmetic and mirror symmetry properties.

Contribution

It determines K3 surfaces with automorphisms of 2-power order matching the transcendental lattice rank, extending previous results and analyzing their arithmetic and mirror symmetry.

Findings

Identified K3 surfaces with automorphisms of 2-power order equal to the transcendental lattice rank.

Analyzed the arithmetic properties of these K3 surfaces.

Commented on the implications for mirror symmetry in this context.

Abstract

This paper concerns complex algebraic K3 surfaces with an automorphism which acts trivially on the Neron-Severi group. Complementing a result by Vorontsov and Kondo, we determine those K3 surfaces where the order of the automorphism is a 2-power and equals the rank of the transcendental lattice. We also study the arithmetic of these K3 surfaces and comment on mirror symmetry