Addendum to the article `Global pluripotential theory over a trivially valued field'

Sebastien Boucksom; Mattias Jonsson

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arXiv · 2206.07183

Addendum to the article `Global pluripotential theory over a trivially valued field'

Sebastien Boucksom·Mattias Jonsson

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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--Amp\`ere energy of a bounded function is equal to the energy of its usc regularized plurisubharmonic envelope.

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Sebastien Boucksom, Mattias Jonsson. 2022-06-14. Addendum to the article `Global pluripotential theory over a trivially valued field'. https://arxiv.org/abs/2206.07183

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