Singular semipositive metrics in non-Archimedean geometry

S. Boucksom; C. Favre; M. Jonsson

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arXiv · 1201.0187

Singular semipositive metrics in non-Archimedean geometry

S. Boucksom·C. Favre·M. Jonsson

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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.

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BibTeX RIS

S. Boucksom, C. Favre, M. Jonsson. 2014-01-21. Singular semipositive metrics in non-Archimedean geometry. https://arxiv.org/abs/1201.0187

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