4 papers
From complex to non-Archimedean geometry: an approach to the YTD conjecture
Sébastien Boucksom, Mattias Jonsson
These notes expand on talks given by the authors at the 2025 Summer Research Institute in Algebraic Geometry in Fort Collins, Colorado. We discuss the relation between algebraic, a…
On the Yau-Tian-Donaldson conjecture for weighted cscK metrics
Sébastien Boucksom, Mattias Jonsson
We establish a version, formulated in terms of non-Archimedean pluripotential theory, of the Yau-Tian-Donaldson conjecture for constant scalar curvature and, more generally, weight…
Weighted extremal Kähler metrics on resolutions of singularities
Sébastien Boucksom, Mattias Jonsson, Antonio Trusiani
Generalizing previous results of Arezzo-Pacard-Singer, Seyyedali-Székelyhidi and Hallam, we prove the invariance under smooth blowups of the class of weighted extremal Kähler manif…
Global pluripotential theory over a trivially valued field
Sébastien Boucksom, Mattias Jonsson
We develop global pluripotential theory in the setting of Berkovich geometry over a trivially valued field. Specifically, we define and study functions and measures of finite energ…