Journal of Differential Geometry

Continuity of extremal transitions and flops for Calabi-Yau manifolds

Xiaochun Rong and Yuguang Zhang

Full-text: Open access

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.

Article information

Source
J. Differential Geom., Volume 89, Number 2 (2011), 233-269.

Dates
First available in Project Euclid: 21 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1324477411

Digital Object Identifier
doi:10.4310/jdg/1324477411

Mathematical Reviews number (MathSciNet)
MR2863918

Zentralblatt MATH identifier
1264.32021

Citation

Rong, Xiaochun; Zhang, Yuguang. Continuity of extremal transitions and flops for Calabi-Yau manifolds. J. Differential Geom. 89 (2011), no. 2, 233--269. doi:10.4310/jdg/1324477411. https://projecteuclid.org/euclid.jdg/1324477411


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