Work

Addendum to the article “Global pluripotential theory over a trivially valued field”

Year: 2024

Type: article

Abstract: This note is an addendum to the paper “Global pluripotential theory over a trivially valued field” by the present authors, in which we prove two results. Let X be an irreducible projective variety over an algebraically closed field field k , and assume that k has characteristic zero, or that X has dimension at most two. We first prove that when X is smooth, the envelope property holds for any numerical class on X . Then we prove that for X possibly singular and for an ample numerical class, the Monge–Ampère energy of a bounded function is equal to the energy of its usc regularized plurisubharmonic envelope.

Source: Annales de la faculté des sciences de Toulouse Mathématiques

DOI: 10.5802/afst.1775

Authors: Sébastien Boucksom, Mattias Jonsson

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: Non-Archimedean Methods in Complex Analysis, Dynamics, and Geometry, Complex Analysis, Dynamics, and Geometry via Non-Archimedean Methods

OpenAlex ID: W4402729754

FWCI: 0.673

Cites: 7

Cited by: 1

Related to: 10