Global pluripotential theory over a trivially valued field
Sébastien Boucksom, Mattias Jönsson
Abstract
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 energy and the non-Archimedean Monge–Ampère operator on any (possibly reducible) projective variety. We also investigate the topology of the space of valuations of linear growth, and the behavior of plurisubharmonic functions thereon.
Topics & Concepts
Variety (cybernetics)MathematicsPure mathematicsTopology (electrical circuits)Field (mathematics)Space (punctuation)Computer scienceCombinatoricsStatisticsOperating systemGeometry and complex manifoldsAlgebraic Geometry and Number TheoryHolomorphic and Operator Theory