Prime order automorphisms of abelian surfaces: a lattice-theoretic point of view

TL;DR

This paper reviews automorphisms of complex 2-tori from a lattice-theoretic perspective, classifying families of symplectic and non-symplectic automorphisms of prime order.

Contribution

It provides a new classification framework for prime order automorphisms of abelian surfaces using lattice theory.

Findings

Classification of symplectic automorphisms

Classification of non-symplectic automorphisms

New insights into automorphism families

Abstract

In this article, we focus on a new perspective of automorphisms of complex 2-tori, reviewing previous works from a lattice-theoretic point of view. In particular, we give a classification of families of symplectic and non-symplectic automorphisms of prime order.