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Sébastien Boucksom; Mattias Jonsson
Tropical and non-Archimedean limits of degenerating families of volume forms
(Limites tropicales et non archimédiennes de familles de formes volumes qui dégénèrent)
Journal de l'École polytechnique — Mathématiques, 4 (2017), p. 87-139, doi: 10.5802/jep.39
Article PDF | TeX source
Class. Math.: 32Q25, 14J32, 14T05, 53C23, 32P05, 14G22
Mots clés: Variétés de Calabi-Yau, formes volumes, dégénérescences, espaces de Berkovich

Résumé - Abstract

Nous étudions le comportement asymptotique de formes volumes dans une famille de variétés complexes compactes qui dégénèrent. Sous des conditions assez générales, nous montrons que les formes volumes convergent en un sens naturel vers une mesure du type de Lebesgue sur un certain complexe simplicial. Ceci fournit en particulier une version en théorie de la mesure d’une conjecture de Kontsevich–Soibelman et Gross–Wilson portant sur les dégénérescences maximales de variétés de Calabi-Yau.

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