期刊
MATHEMATISCHE ZEITSCHRIFT
卷 299, 期 3-4, 页码 2341-2378出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00209-021-02770-2
关键词
Non-Archimedean geometry; Berkovich spaces; Pluripotential theory; Monge-Ampere operators
类别
资金
- European Research Council Advanced Grant ALKAGE (Algebraic and Kahler Geometry)
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.
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.
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