I study pluripotential theory on Berkovich spaces.
Keywords: non-Archimedean geometry, algebraic geometry, Berkovich spaces, pluripotential theory.
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.
A Berkovich space, caught in the wild and taxidermied: