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K-stability of constant scalar curvature polarization

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arxiv 0812.4093 v2 pith:FPHEBCZO submitted 2008-12-22 math.DG math.AG

Toshiki Mabuchi This is my paper · ORCID
classification math.DGmath.AG
keywords constantcurvaturek-stabilitypolarizationscalaradmitsalgebraicarguments
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In this paper, we shall show that a polarized algebraic manifold is K-stable if the polarization class admits a Kaehler metric of constant scalar curvature. This generalizes the results of Chen-Tian, Donaldson and Stoppa. (Parts of the arguments are based on a forthcoming paper "A stronger concept of K-stability." )

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  1. A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations

    math.AG 2026-05 unverdicted novelty 7.0 of 10

    Any big line bundle admits a special Fujita approximation, which is used to solve the uniform Yau-Tian-Donaldson conjecture: a polarized smooth projective variety admits a cscK metric iff it is Aut°(X,L)-uniformly K-stable.

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