On the K-stability of Fano varieties and anticanonical divisors

Abstract

We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical Q-divisors. First, we propose a condition in terms of certain anticanonical Q-divisors of given Fano variety, which we conjecture to be equivalent to the K-stability. We prove that it is at least sufficient condition and also relate to the Berman-Gibbs stability. We also give another algebraic proof of the K-stability of Fano varieties which satisfy Tian's alpha invariants condition.

13 pages. Final version, to appear in Tohoku Math Journal

Cited by in corpus (5)

• K-stability of smooth del Pezzo surfaces
• Explicit Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds
• Higher Codimensional Alpha Invariants and Characterization of Projective Spaces
• An algebraic proof of K-semistability of the projective plane
• Product Theorem for K-stability