Some non-Archimedean pluripotential theory on polarized affine cones
Yueqiao Wu
TL;DR
This paper explores non-Archimedean pluripotential theory on polarized affine cones, extending concepts like plurisubharmonic functions and the Monge--Ampère operator from projective varieties to affine cones over trivially valued fields.
Contribution
It introduces a framework for non-Archimedean pluripotential theory on polarized affine cones, generalizing existing results from projective varieties.
Findings
Defined plurisubharmonic functions on affine cones
Extended the Monge--Ampère operator to finite energy classes
Partially generalized Boucksom--Jonsson's results
Abstract
We undertake a preliminary step towards studying non-Archimedean pluripotential theory on polarized affine cones over a trivially valued field. We study plurisubharmonic functions and the Monge--Amp\`ere operator defined on the finite energy class, partially generalizing a result of Boucksom--Jonsson on projective varieties.
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Taxonomy
Topicsadvanced mathematical theories · Algebraic and Geometric Analysis · Stochastic processes and financial applications