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

Given an ample line bundle L over a projective K-variety X, with K 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.

Automated summary

In this study, we examine the limits of non-Archimedean metrics on a projective K-variety X equipped with an ample line bundle L, and show that there is a one-to-one correspondence between equivalence classes of bounded graded norms and bounded plurisubharmonic metrics that are regularizable from below. This generalizes previous results and expands the understanding of the problem in a rather general case.