The maximal destabilizers for Chow and K-stability
2025/11/20 by Yao, Yi
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory
paper · doi:10.48550/arxiv.2511.16401
Abstract
Donaldson showed that the constant scalar curvature Kähler metrics can be quantized by the balanced Hermitian norms on the spaces of global sections. We explore an analogous problem in the unstable situation. For a K-unstable manifold (X,L), its projective embedding via |kL| will be Chow-unstable when k is sufficiently large and divisible. There is a unique filtration on H0(X,kL), that corresponds to the maximal destabilizer for Chow-stability of the embedded variety. On the other hand, there is a maximal destabilizer for K-stability after the work of Xia and Li, which corresponds to the steepest descent direction of K-energy. Based on Boucksom-Jonsson's non-Archimedean pluripotential theory and some idealistic assumptions, we provide a route to show that maximal K-destabilizers are quantized by the maximal Chow-destabilizers.
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