The classification of smooth quotients of abelian surfaces

TL;DR

This paper classifies smooth projective surfaces obtained as quotients of abelian surfaces by finite groups, providing a comprehensive understanding of their structure and properties.

Contribution

It offers a complete classification of smooth quotients of abelian surfaces, filling a gap in the understanding of their geometric and algebraic structure.

Findings

Identifies all possible smooth quotient surfaces of abelian surfaces.

Provides explicit descriptions of the quotient surfaces.

Establishes criteria for smoothness in these quotients.

Abstract

We classify smooth projective surfaces that are quotients of abelian surfaces by finite groups.