Gromov-Hausdorff collapsing of Calabi-Yau manifolds

Mark Gross, Valentino Tosatti, Yuguang Zhang

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

This paper is a sequel to [12]. We further study Gromov-Hausdorff collapsing limits of Ricci-flat Kähler metrics on abelian fibered Calabi-Yau manifolds. Firstly, we show that in the same setup as [12], if the dimension of the base manifold is one, the limit metric space is homeomorphic to the base manifold. Secondly, if the fibered Calabi-Yau manifolds are Lagrangian fibrations of holomorphic symplectic manifolds, the metrics on the regular parts of the limits are special Kähler metrics. By combining these two results, we extend [13] to any fibered projective K3 surface without any assumption on the type of singular fibers.

Original languageEnglish (US)
Pages (from-to)93-113
Number of pages21
JournalCommunications in Analysis and Geometry
Volume24
Issue number1
DOIs
StatePublished - Jan 1 2016

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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