# Rationally elliptic toric varieties

## TL;DR

This paper characterizes complete smooth toric varieties with elliptic rational homotopy type and explicitly describes all such varieties in complex dimensions up to three.

## Contribution

It provides a complete characterization and explicit descriptions of rationally elliptic smooth toric varieties in low dimensions.

## Key findings

- Characterization of all such toric varieties
- Explicit descriptions in dimensions up to three
- Identification of elliptic rational homotopy types

## Abstract

We give a characterization of all complete smooth toric varieties whose rational homotopy is of elliptic type. All such toric varieties of complex dimension not more than three are explicitly described.