Alpha invariants and K-stability for general polarisations of Fano varieties
arXiv:1307.6527
Abstract
We provide a sufficient condition for polarisations of Fano varieties to be K-stable in terms of Tian's alpha invariant, which uses the log canonical threshold to measure singularities of divisors in the linear system associated to the polarisation. This generalises a result of Odaka-Sano in the anti-canonically polarised case, which is the algebraic counterpart of Tian's analytic criterion implying the existence of a Kähler-Einstein metric. As an application, we give new K-stable polarisations of a general degree one del Pezzo surface. We also prove a corresponding result for log K-stability.
21 pages, published version
References in corpus (6)
- K-stability and Kähler-Einstein metrics
- Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
- Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
- Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities
- Asymptotically log Fano varieties
- K-stability of constant scalar curvature Kähler manifolds