The Zariski-Lipman conjecture for toric varieties

TL;DR

This paper provides a concise proof of the Zariski-Lipman conjecture specifically for toric varieties, establishing that a toric variety with a locally free tangent sheaf must be smooth.

Contribution

It offers a new, simplified proof of the conjecture for toric varieties, confirming the smoothness condition under the locally free tangent sheaf assumption.

Findings

Toric varieties with locally free tangent sheaf are smooth.

The proof simplifies understanding of the Zariski-Lipman conjecture in the toric case.

The result confirms the conjecture for a broad class of algebraic varieties.

Abstract

We give a short proof of the Zariski-Lipman conjecture for toric varieties: any complex toric variety with locally free tangent sheaf is smooth.