A Fulton-Hansen theorem for almost homogeneous spaces

TL;DR

This paper generalizes the Fulton-Hansen connectedness theorem to a broader class of varieties with dense group actions, extending its applicability beyond projective spaces.

Contribution

It introduces a new version of the theorem applicable to almost homogeneous spaces with algebraic group actions, broadening the scope of the original result.

Findings

Generalized connectedness theorem for normal varieties with dense group actions

Applicable to almost homogeneous spaces beyond projective spaces

Provides new tools for studying algebraic group actions on varieties

Abstract

We prove a generalization of the Fulton-Hansen connectedness theorem, where ${\mathbb P}^n$ is replaced by a normal variety on which an algebraic group acts with a dense orbit.