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Solution to a non-Archimedean Monge-Amp'ere equation | S. Boucksom
; C. Favre
; M. Jonsson
; | Date: |
30 Dec 2011 | Abstract: | Let X be a smooth projective Berkovich space over a complete discrete
valuation field K of residue characteristic zero, and assume that X is defined
over a function field admitting K as a completion. Let further m be a positive
measure on X and L be an ample line bundle such that the mass of m is equal to
the degree of L. Then we show the existence a continuous semipositive metric
whose associated measure is equal to m in the sense of Zhang and Chambert-Loir.
This we do under a technical assumption on the support of m, which is, for
instance, fulfilled if the support is a finite set of divisorial points. Our
method draws on analogues of the variational approach developed to solve
complex Monge-Amp’ere equations on compact K"ahler manifolds by Berman,
Guedj, Zeriahi and the first named author, and of Ko{l}odziej’s continuity
estimates. It relies in a crucial way on the compactness properties of singular
semipositive metrics, as defined and studied in a companion article. | Source: | arXiv, 1201.0188 | Services: | Forum | Review | PDF | Favorites |
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