Abelian varieties as automorphism groups of smooth projective varieties

TL;DR

This paper investigates which complex abelian varieties can serve as the automorphism groups of smooth projective varieties, providing a classification of such varieties based on their automorphism group structures.

Contribution

It characterizes the abelian varieties that can be realized as automorphism groups of smooth projective varieties, offering a classification framework.

Findings

Identifies conditions under which abelian varieties are automorphism groups

Provides a classification of abelian varieties as automorphism groups

Advances understanding of automorphism group structures in algebraic geometry

Abstract

We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.