Optimal destabilizing centers and equivariant K-stability

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.

23 pages. v3: minor revision following referee's comments. To appear in Invent. Math

References in corpus (2)

• K-stability of log Fano hyperplane arrangements
• On properness of K-moduli spaces and optimal degenerations of Fano varieties

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• Sharp bounds on the height of K-semistable Fano varieties I, the toric case
• Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability
• On K-stability of Fano weighted hypersurfaces
• Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII