SINGULAR SEMIPOSITIVE METRICS IN NON-ARCHIMEDEAN GEOMETRY

被引：47

作者：

Boucksom, Sebastien ^{[1
,2
]}

Favre, Charles ^{[2
]}

Jonsson, Mattias ^{[3
]}

机构：

[1] Univ Paris 06, CNRS, Inst Math, F-75251 Paris 05, France

[2] Ecole Polytech, CNRS, CMLS, F-91128 Palaiseau, France

[3] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

JOURNAL OF ALGEBRAIC GEOMETRY | 2016年 / 25卷 / 01期

基金：

美国国家科学基金会; 欧洲研究理事会;

关键词：

ASYMPTOTIC INVARIANTS; BERKOVICH SPACES; VALUATIONS; VARIETIES; HEIGHTS; IDEALS;

D O I：

10.1090/jag/656

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 scaling, 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.

引用

页码：77 / 139

页数：63