A variational approach to the Yau-Tian-Donaldson conjecture
Differential Geometry
2020-09-09 v3 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1509.04561,
title = {A variational approach to the Yau-Tian-Donaldson conjecture},
author = {Robert Berman and Sébastien Boucksom and Mattias Jonsson},
journal= {arXiv preprint arXiv:1509.04561},
year = {2020}
}
Comments
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