Variational and non-Archimedean aspects of the Yau--Tian--Donaldson\n conjecture

2018/05/08 by Sébastien Boucksom, Boucksom, Sébastien · 3 citations
Mathematics · Physics and Astronomy · #58E11 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1805.03289

openalex publication_date 2018/05/08 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We survey some recent developments in the direction of the Yau-Tian-Donaldson\nconjecture, which relates the existence of constant scalar curvature K "ahler\nmetrics to the algebro-geometric notion of K-stability. The emphasis is put on\nthe use of pluripotential theory and the interpretation of K-stability in terms\nof non-Archimedean geometry.\n

Cited by

• The maximal destabilizers for Chow and K-stability
• High Energy plurisubharmonic classes
• Filtrations and asymptotic geometry of non-Archimedean norms on section rings

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