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October 2011 Continuity of extremal transitions and flops for Calabi-Yau manifolds
Xiaochun Rong, Yuguang Zhang
J. Differential Geom. 89(2): 233-269 (October 2011). DOI: 10.4310/jdg/1324477411

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.

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Xiaochun Rong. Yuguang Zhang. "Continuity of extremal transitions and flops for Calabi-Yau manifolds." J. Differential Geom. 89 (2) 233 - 269, October 2011. https://doi.org/10.4310/jdg/1324477411

Information

Published: October 2011
First available in Project Euclid: 21 December 2011

zbMATH: 1264.32021
MathSciNet: MR2863918
Digital Object Identifier: 10.4310/jdg/1324477411

Rights: Copyright © 2011 Lehigh University

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Vol.89 • No. 2 • October 2011
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