On the effective YTD conjecture

2025/09/10 by Delcroix, Thibaut
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.08760

Abstract

We formulate an effective variant of the Yau-Tian-Donaldson conjecture, then review effective results on K-stability of spherical varieties, that is, K-stability criterions which can be effectively computed given the combinatorial data associated with the variety. We focus on the standard notion of K-stability as defined by Donaldson for constant scalar curvature Kähler metrics.

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Related

• Variational and non-Archimedean aspects of the Yau--Tian--Donaldson\n conjecture
• On K-Stability of Reductive Varieties
• K-stability for Kähler Manifolds
• A relative Yau-Tian-Donaldson conjecture and stability thresholds
• CscK metrics on rank one spherical Fano fourfolds