Singular semipositive metrics in non-Archimedean geometry

Details Singular semipositive metrics in non-Archimedean geometry Singular semipositive metrics in non-Archimedean geometry

2011-12-30

arxiv.org/abs/1201.0187v1

Mathematics

Algebraic Geometry

45 pages, 1 figure

Scientific paper

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.

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