Radiant toric varieties and unipotent group actions

TL;DR

This paper characterizes certain complete toric varieties where a maximal unipotent subgroup acts with an open orbit, analyzing their Demazure roots and subgroup structures to understand their automorphism groups.

Contribution

It provides a detailed characterization of toric varieties with unipotent automorphism groups acting with an open orbit, including structure and subgroup classifications.

Findings

Characterization of varieties via Demazure roots

Description of maximal unipotent subgroup structure

Identification of regular subgroups with open orbit actions

Abstract

We consider complete toric varieties $X$ such that a maximal unipotent subgroup $U$ of the automorphism group $\text{Aut}(X)$ acts on $X$ with an open orbit. It turns out that such varieties can be characterized by several remarkable properties. We study the set of Demazure roots of the corresponding complete fan, describe the structure of a maximal unipotent subgroup $U$ in $\text{Aut}(X)$, and find all regular subgroups in $U$ that act on $X$ with an open orbit.