# K-semistable Fano manifolds with the smallest alpha invariant

## TL;DR

This paper proves that among K-semistable Fano manifolds, those with the minimal alpha invariant are necessarily projective spaces, and also explores related singular cases.

## Contribution

It establishes a characterization of K-semistable Fano manifolds with minimal alpha invariant as projective spaces, including singular cases.

## Key findings

- K-semistable Fano manifolds with smallest alpha invariant are projective spaces
- Singular cases of such manifolds are also characterized
- Provides a classification result in Fano geometry

## Abstract

In this short note, we show that K-semistable Fano manifolds with the smallest alpha invariant are projective spaces. Singular cases are also investigated.