K-stability of Fano manifolds with not small alpha invariants

Abstract

We show that any $n$-dimensional Fano manifold $X$ with $\alpha (X)=n/(n+1)$ and $n\ge 2$ is K-stable, where $\alpha (X)$ is the alpha invariant of $X$ introduced by Tian. In particular, any such $X$ admits Kähler-Einstein metrics and the holomorphic automorphism group of $X$ is finite.

arXiv comment12 pages

References in corpus (5)

• A generalization of Ross-Thomas' slope theory
• K-stability of constant scalar curvature polarization
• A stronger concept of K-stability
• Finite generation and geography of models
• A valuative criterion for uniform K-stability of $\mathbb{Q}$-Fano varieties

Cited by in corpus (3)

• K-stability of log Fano hyperplane arrangements
• Explicit Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds
• Product Theorem for K-stability