On Picard Number and Dimension of Algebraic Homogeneous Spaces

TL;DR

This paper establishes inequalities relating the dimension and Picard number of algebraic homogeneous spaces, providing new insights into their geometric structure.

Contribution

It introduces inequalities connecting the dimension and Picard number of homogeneous spaces under linear algebraic groups, advancing understanding of their geometric properties.

Findings

Derived bounds linking dimension and Picard number.

Enhanced understanding of the structure of algebraic homogeneous spaces.

Potential applications to classification problems.

Abstract

An algebraic variety $X$ is called a homogeneous space if there exists a transitive regular action of an algebraic group on $X$. We prove inequalities between the dimension of a homogeneous space of a linear algebraic group and its Picard number.