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Continuity of extremal transitions and flops for calabi–yau manifolds

Xiaochun Rong Capital Normal University Yuguang Zhang Capital Normal University

Differential Geometry mathscidoc:1609.10240

Journal of Differential Geometry, 89, (2), 233-269, 2011
In this paper, we study the behavior of Ricci-flat K¨ahler 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 K¨ahler metrics on Calabi–Yau manifolds along a smoothing is established, which can be of independent interest.
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@inproceedings{xiaochun2011continuity,
  title={CONTINUITY OF EXTREMAL TRANSITIONS AND FLOPS FOR CALABI–YAU MANIFOLDS},
  author={Xiaochun Rong, and Yuguang Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913210607290579901},
  booktitle={Journal of Differential Geometry},
  volume={89},
  number={2},
  pages={233-269},
  year={2011},
}
Xiaochun Rong, and Yuguang Zhang. CONTINUITY OF EXTREMAL TRANSITIONS AND FLOPS FOR CALABI–YAU MANIFOLDS. 2011. Vol. 89. In Journal of Differential Geometry. pp.233-269. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913210607290579901.
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