The asymptotic Fubini-Study operator over general non-Archimedean fields

2020/04/24 by Reboulet, Rémi · 2 citations
#14G22 #32PO5 #32U05 #32U15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.11635

Abstract

Given an ample line bundle L over a projective \mathbbK-variety X, with \mathbbK a non-Archimedean field, we study limits of non-Archimedean metrics on L associated to submultiplicative sequences of norms on the graded pieces of the section ring R(X,L). We show that in a rather general case, the corresponding asymptotic Fubini-Study operator yields a one-to-one correspondence between equivalence classes of bounded graded norms and bounded plurisubharmonic metrics that are regularizable from below. This generalizes results of Boucksom-Jonsson where this problem has been studied in the trivially valued case.

Cited by

• Metrized ample line bundles in non-Archimedean geometry II
• Filtrations and asymptotic geometry of non-Archimedean norms on section rings

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