On uniqueness of additive actions on complete toric varieties

TL;DR

This paper establishes a criterion to determine when an additive action on a complete toric variety is unique, contributing to the understanding of group actions in algebraic geometry.

Contribution

It provides the first known criterion for the uniqueness of additive actions specifically on complete toric varieties.

Findings

A clear criterion for the uniqueness of additive actions on complete toric varieties.

Characterization of additive actions with open orbits on these varieties.

Insights into the structure of unipotent group actions in algebraic geometry.

Abstract

By an additive action on an algebraic variety $X$ we mean a regular effective action $\mathbb{G}_a^n\times X\to X$ with an open orbit of the commutative unipotent group $\mathbb{G}_a^n$. In this paper, we give a uniqueness criterion for additive action on a complete toric variety.