Affiliation:
1. Institut Fourier , Université Grenoble Alpes , 100 Rue des Mathématiques, 38610 , Gières , France
Abstract
Abstract
Given a polarized projective variety
(
X
,
L
)
{(X,L)}
over any non-Archimedean field, assuming continuity of envelopes, we define a metric on the space of finite-energy metrics on L, related to a construction of Darvas in the complex setting. We show that this makes finite-energy metrics on L into a geodesic metric space, where geodesics are given as maximal psh segments. Given two continuous psh metrics, we show that the maximal segment joining them is furthermore continuous. Our results hold in particular in all situations relevant to the study of degenerations and K-stability in complex geometry.
Subject
Applied Mathematics,General Mathematics
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