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Pré-Publication, Document De Travail Année : 2023

NON-ARCHIMEDEAN GREEN'S FUNCTIONS AND ZARISKI DECOMPOSITIONS

Résumé

We study the non-Archimedean Monge-Ampère equation on a smooth projective variety over a discretely or trivially valued field. First, we give an example of a Green's function, associated to a divisorial valuation, which is not Q-PL (i.e. not a model function in the discretely valued case). Second, we produce an example of a function whose Monge-Ampère measure is a finite atomic measure supported in a dual complex, but which is not invariant under the retraction associated to any snc model. This answers a question by Burgos Gil et al in the negative. Our examples are based on geometric constructions by Cutkosky and Lesieutre, and arise via base change from Green's functions over a trivially valued field; this theory allows us to efficiently encode the Zariski decomposition of a pseudoeffective numerical class.
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Dates et versions

hal-04272871 , version 1 (06-11-2023)

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  • HAL Id : hal-04272871 , version 1

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Sébastien Boucksom, Mattias Jonsson. NON-ARCHIMEDEAN GREEN'S FUNCTIONS AND ZARISKI DECOMPOSITIONS. 2023. ⟨hal-04272871⟩
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