Optimal destabilizing centers and equivariant K-stability
arXiv:2004.09413 · doi:10.1007/s00222-021-01046-0
Abstract
We give an algebraic proof of the equivalence of equivariant K-semistability (resp. equivariant K-polystability) with geometric K-semistability (resp. geometric K-polystability). Along the way we also prove the existence and uniqueness of minimal optimal destabilizing centers on K-unstable log Fano pairs.
arXiv comment23 pages. v3: minor revision following referee's comments. To appear in Invent. Math
References in corpus (8)
- A generalization of Ross-Thomas' slope theory
- K-semistability is equivariant volume minimization
- Reductivity of the automorphism group of K-polystable Fano varieties
- Uniform K-stability and plt blowups of log Fano pairs
- On positivity of the CM line bundle on K-moduli spaces
- K-stability of log Fano hyperplane arrangements
- K-stability of smooth del Pezzo surfaces
- On properness of K-moduli spaces and optimal degenerations of Fano varieties
Cited by in corpus (13)
- Reductivity of the automorphism group of K-polystable Fano varieties
- Algebraicity of the Metric Tangent Cones and Equivariant K-stability
- Optimal destabilization of K-unstable Fano varieties via stability thresholds
- Basis divisors and balanced metrics
- On properness of K-moduli spaces and optimal degenerations of Fano varieties
- On K-stability of some del Pezzo surfaces of Fano index 2
- K-stability of cubic fourfolds
- On sharp lower bounds for Calabi type functionals and destabilizing properties of gradient flows
- A Note on Equivariant K-stability
- Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability
- Sharp bounds on the height of K-semistable Fano varieties I, the toric case
- Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
- On K-stability of Fano weighted hypersurfaces