Continuity of extremal transitions and flops for calabi–yau manifolds

Xiaochun Rong, Yuguang Zhang

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

In this paper, we study the behavior of Ricci-flat Kähler metrics on Calabi–Yau manifolds under algebraic geometric surgeries: extremal transitions or flops. We prove a version of Candelas and de la Ossa’s conjecture: Ricci–flat Calabi–Yau manifolds related by extremal transitions and flops can be connected by a path consisting of continuous families of Ricci-flat Calabi–Yau manifolds and a compact metric space in the Gromov–Hausdorff topology. In an essential step of the proof of our main result, the convergence of Ricci–flat Kähler metrics on Calabi–Yau manifolds along a smoothing is established, which can be of independent interest.

Original languageEnglish (US)
Pages (from-to)233-269
Number of pages37
JournalJournal of Differential Geometry
Volume89
Issue number2
DOIs
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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