[Convergence hybride de mesures de Kähler–Einstein]
Nous calculons la limite hybride (au sens de Boucksom–Jonsson) de la famille des formes volumes de Kähler–Einstein sur une dégénérescence de variétés canoniquement polarisées. La mesure limite est une somme pondérée de masses de Dirac en des valuations divisorielles, déterminées par la limite algébro-géométrique naturelle de la famille. Nous formulons aussi des remarques sur l’opérateur de Monge–Ampère non-archimédien et la continuité hybride des potentiels de Kähler–Einstein dans ce contexte.
We compute the hybrid limit (in the sense of Boucksom–Jonsson) of the family of Kähler–Einstein volume forms on a degeneration of canonically polarized manifolds. The limit measure is a weighted sum of Dirac masses at divisorial valuations, determined by the natural algebro-geometric limit of the family. We also make some remarks on the non-archimedean Monge–Ampère operator and hybrid continuity of Kähler–Einstein potentials in this context.
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DOI : 10.5802/aif.3455
Keywords: Kähler–Einstein manifolds, degenerations, Berkovich spaces
Mot clés : Variétés de Kähler–Einstein, dégénérescences, espaces de Berkovich
CC-BY-ND 4.0
@article{AIF_2022__72_2_587_0,
author = {Pille-Schneider, L\'eonard},
title = {Hybrid convergence of {K\"ahler{\textendash}Einstein} measures},
journal = {Annales de l'Institut Fourier},
pages = {587--615},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {72},
number = {2},
year = {2022},
doi = {10.5802/aif.3455},
zbl = {07554664},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3455/}
}
TY - JOUR AU - Pille-Schneider, Léonard TI - Hybrid convergence of Kähler–Einstein measures JO - Annales de l'Institut Fourier PY - 2022 SP - 587 EP - 615 VL - 72 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3455/ DO - 10.5802/aif.3455 LA - en ID - AIF_2022__72_2_587_0 ER -
%0 Journal Article %A Pille-Schneider, Léonard %T Hybrid convergence of Kähler–Einstein measures %J Annales de l'Institut Fourier %D 2022 %P 587-615 %V 72 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3455/ %R 10.5802/aif.3455 %G en %F AIF_2022__72_2_587_0
Pille-Schneider, Léonard. Hybrid convergence of Kähler–Einstein measures. Annales de l'Institut Fourier, Tome 72 (2022) no. 2, pp. 587-615. doi : 10.5802/aif.3455. https://aif.centre-mersenne.org/articles/10.5802/aif.3455/
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