A VARIATIONAL APPROACH TO THE YAU-TIAN-DONALDSON CONJECTURE
| Autor: | Berman, Robert, Boucksom, S��bastien, Jonsson, Mattias |
|---|---|
| Přispěvatelé: | Department of Mathematical Sciences (Chalmers), Chalmers University of Technology [Göteborg], Centre de Mathématiques Laurent Schwartz (CMLS), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Department of Mathematics, University of Michigan [Ann Arbor], University of Michigan System-University of Michigan System, Boucksom, Sebastien |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Differential Geometry (math.DG) Mathematics::Complex Variables FOS: Mathematics [MATH] Mathematics [math] Mathematics::Differential Geometry [MATH]Mathematics [math] 53C55 14J45 32P05 32Q20 32Q26 Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry |
| Popis: | We give a variational proof of a version of the Yau-Tian-Donaldson conjecture for twisted K\"ahler-Einstein currents, and use this to express the greatest (twisted) Ricci lower bound in terms of a purely algebro-geometric stability threshold. Our approach does not involve the continuity method or Cheeger-Colding-Tian theory, and uses instead pluripotential theory and valuations. Along the way, we study the relationship between geodesic rays and non-Archimedean metrics. Comment: Added Appendix B on a valuative analysis of singularities of plurisubharmonic functions. Various other small changes and improvements. To appear in Journal of the AMS |
| Databáze: | OpenAIRE |
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