Tropical and non-Archimedean limits of degenerating families of volume forms

We study the asymptotic behavior of volume forms on a degenerating family of compact complex manifolds. Under rather general conditions, we prove that the volume forms converge in a natural sense to a Lebesgue-type measure on a certain simplicial complex. In particular, this provides a measure-theor...

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Bibliographic Details
Published inJournal de l'École polytechnique. Mathématiques Vol. 4; pp. 87 - 139
Main Authors Boucksom, Sébastien, Jonsson, Mattias
Format Journal Article
LanguageEnglish
Published École polytechnique 01.01.2017
Subjects
Berkovich spaces
Calabi-Yau manifolds
Degenerations
Matematik
Mathematical sciences
Mathematics
Volume forms
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ISSN2429-7100
2270-518X
2270-518X
DOI10.5802/jep.39

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Summary:We study the asymptotic behavior of volume forms on a degenerating family of compact complex manifolds. Under rather general conditions, we prove that the volume forms converge in a natural sense to a Lebesgue-type measure on a certain simplicial complex. In particular, this provides a measure-theoretic version of a conjecture by Kontsevich–Soibelman and Gross–Wilson, bearing on maximal degenerations of Calabi–Yau manifolds.
ISSN:2429-7100
2270-518X
2270-518X
DOI:10.5802/jep.39