Singular semipositive metrics in non-Archimedean geometry

Abstract

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or plurisubharmonic) metrics on L, and prove the analogue of the following two basic results in the complex case: the set of semipositive metrics is compact modulo constants, and each semipositive metric is a decreasing limit of smooth semipositive ones. In particular, for continuous metrics our definition agrees with the one by S.-W. Zhang. The proofs use multiplier ideals and the construction of suitable models of X over the valuation ring of K, using toroidal techniques.

49 pages, 1 figure. Accepted in the Journal of Algebraic Geometry

References in corpus (5)

• The tropicalization of the moduli space of curves
• Desingularization of quasi-excellent schemes in characteristic zero
• Formes différentielles réelles et courants sur les espaces de Berkovich
• Non-archimedean tame topology and stably dominated types
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• On the structure of nonarchimedean analytic curves
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• Invariants of Varieties and Singularities inspired by Kahler-Einstein problems
• Degenerations of amoebae and Berkovich spaces
• On the Berkovich double residue fields and birational models