Tropical and non-archimedean limits of degenerating families of volume forms
Artikel i vetenskaplig tidskrift, 2017

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.

Volume forms

Degenerations

Calabi-Yau manifolds

Berkovich spaces

Författare

Sebastien Boucksom

Centre de Mathematiques Laurent Schwartz Ecole polytechnique

Mattias Jonsson

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Journal de l'Ecole Polytechnique - Mathematiques

24297100 (ISSN) 2270518X (eISSN)

Vol. 4 87-139

Ämneskategorier

Matematik