Toric varieties admitting an action of a unipotent group with a finite number of orbits

TL;DR

This paper classifies complete simplicial toric varieties that admit a unipotent group action with finitely many orbits, providing a full list in the two-dimensional case.

Contribution

It offers a complete characterization of such toric varieties and explicitly lists all two-dimensional cases.

Findings

Classification of complete simplicial toric varieties with unipotent group actions

Explicit list of two-dimensional cases

Finite orbit property under unipotent group actions

Abstract

We describe complete simplicial toric varieties on which a unipotent group acts with a finite number of orbits. We also provide a complete list of such varieties in the case where the dimension is equal to 2.