Log Kodaira dimension of homogeneous varieties

TL;DR

This paper characterizes when the log Kodaira dimension of a complex homogeneous variety is non-negative, establishing it as equivalent to the variety being a semi-abelian variety.

Contribution

It provides a precise criterion linking the log Kodaira dimension to the structure of homogeneous varieties, specifically identifying semi-abelian varieties.

Findings

Log Kodaira dimension is non-negative iff the variety is semi-abelian.

Provides a characterization of homogeneous varieties based on their log Kodaira dimension.

Establishes a clear criterion connecting algebraic structure and geometric invariants.

Abstract

Let $V$ be a complex algebraic variety, homogeneous under the action of a complex algebraic group. We show that the log Kodaira dimension of $V$ is non-negative if and only if $V$ is a semi-abelian variety.