A valuative criterion for uniform K-stability of $\mathbb{Q}$-Fano varieties

TL;DR

This paper establishes a straightforward criterion to determine uniform K-stability of $ ext{Q}$-Fano varieties, simplifying the process of verifying their stability in algebraic geometry.

Contribution

It provides a simple necessary and sufficient valuative criterion for uniform K-stability of $ ext{Q}$-Fano varieties, advancing the understanding of their stability conditions.

Findings

A new valuative criterion for uniform K-stability.

Simplification of stability verification process.

Clear necessary and sufficient conditions established.

Abstract

We give a simple necessary and sufficient condition for uniform K-stability of $\mathbb{Q}$-Fano varieties.