# Cyclic Symmetry on Complex Tori and Bagnera-De Franchis Manifolds

## TL;DR

This paper classifies cyclic group actions on complex tori and applies the results to structure theorems for Bagnera-De Franchis manifolds and hypergeometric integrals, advancing understanding of symmetries in complex geometry.

## Contribution

It provides a detailed description of cyclic group actions on complex tori and establishes a new structure theorem for Bagnera-De Franchis manifolds.

## Key findings

- Classification of cyclic group actions on complex tori
- A new structure theorem for Bagnera-De Franchis manifolds
- Applications to hypergeometric integrals

## Abstract

We describe the possible linear actions of a cyclic group $G = \mathbb{Z} /n$ on a complex torus, using the cyclotomic exact sequence for the group algebra $\mathbb{Z} [G]$. The main application is devoted to a structure theorem for Bagnera-De Franchis Manifolds, but we also give an application to hypergeometric integrals.