# Additive actions on complete toric surfaces

## TL;DR

This paper classifies additive actions of the group ^n on complete toric surfaces, providing a comprehensive understanding of such symmetries in algebraic geometry.

## Contribution

It offers the first complete classification of additive actions specifically on complete toric surfaces, expanding the understanding of unipotent group actions.

## Key findings

- Classification of additive actions on all complete toric surfaces
- Identification of conditions for the existence of additive actions
- Explicit descriptions of additive actions in specific cases

## 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 classification of additive actions on complete toric surfaces.