Global pluripotential theory over a trivially valued field

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-Ampere operator on any (possibly reducible) projective variety. We also investigate the topology of the space of valuations of linear growth, and the behavior of psh functions thereon.

arXiv comment143 pages, 1 figure. Various improvements, psh functions now defined and studied relative to any (not necessarily ample) class. Final version, to appear in Ann. Fac. Sci. Toulouse