Limits of Calabi-Yau metrics when the Kähler class degenerates

Valentino Tosatti*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We study the behavior of families of Ricci-flat Kähler metrics on a projective Calabi-Yau manifold when the Kähler classes degenerate to the boundary of the ample cone.We prove that if the limit class is big and nef the Ricci-flat metrics converge smoothly on compact sets outside a subvariety to a limit incomplete Ricci-flat metric. The limit can also be understood from algebraic geometry.

Original languageEnglish (US)
Pages (from-to)755-776
Number of pages22
JournalJournal of the European Mathematical Society
Issue number4
StatePublished - 2009


  • Calabi-Yau manifolds
  • Degenerate complex Monge-Ampère equations
  • Ricci-flat metrics

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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